Much confusion has arisen over dates from January 1 to March 24, inclusive, prior to 1753, because to and including the year 1752, the first day of the new year was March 25 instead of January 1. Consequently old style March 24, 1750, for instance, was the day before March 25, 1751; and January 1, 1750, was the day after December 31, 1750, and not the day after December 31, 1749.

So that's quite clear now ...

"The Thames OR Graphic illustrations of Seats, Villas, Public Buildings, and Picturesque Scenery" by William Bernard Cooke, 1811 -

[Westminster Bridge] is considered to be one of the finest bridges in the world.

The first stone was laid on the 29th January, 1738, by the then Earl of Pembroke, a great judge, with an uncommon practical knowledge of architecture. The last stone of it was laid on the 20th November, 1750. It was built by Mr. Laberly, a Swiss architect, and consists of thirteen semicircular arches, besides a very small one at each end. The ascent to it is very easy as there is a semi-octangular recess at every pier. The two middle and two extreme ones on each side are covered, as places of shelter to the passengers.
These are the dimensions of this noble structure:

This bridge was built with uncommon attention to its foundation, materials, and mechanical construction. The materials of the piers are much superior to those generally used on such occasions. They are the same within as without, and consist of solid blocks of Portland stone, many of which are four or five tons weight, and are fastened with iron cramps, so concealed and covered as not to be affected by the water. The soffit of every arch is turned and built quite through the same as the fronts; in short, the whole is so contrived, that each arch may be said to stand singly, without affecting or being affected by any of the others. Between every two arches there is also a drain to prevent the water and filth from accumulating.
Eleven years and nine months were employed in erecting this magnificent structure, and the expense of it amounted to three hundred and eighty-nine thousand five hundred pounds: part of which was raised by lotteries, and the rest granted by parliament.

1740? Westminster Bridge under construction -

Westminster Bridge under construction, 1740?

1741: Westminster Bridge Construction –

Westminster Bridge Construction Support Timbers.

One of the design criteria was to allow boats to use the bridge whilst it was being built.  Notice that all the timbers are straight (except those in contact with the stone)   Canaletto failed to notice that and painted them curved –

View under Westminster Bridge, Canaletto

Westminster Bridge.

This bridge was esteemed one of the most complete and elegant structures of the kind in the world. It is built entirely of stone, and extends over the river at a place where it is 1,223 feet broad, which is above 300 feet broader than at London Bridge. On each side is a fine balustrade of stone, with places of shelter from the rain. The width of the bridge is 44 feet, having on each side a fine Footway for passengers. It consisting of fourteen piers, and thirteen large and two small arches, all semicircular, that in the centre being 76 feet wide, and the rest decreasing four feet each from the other; so that the two last arches of the thirteen great ones are each 52 feet. It is computed that £40,000 value in stone and other materials is always under water.
This magnificent structure was begun in 1739, and was finished in 1750, at the expense of £389,000 defrayed by parliament.
It was built after a design of Mons. Labelye, an ingenious French architect.

Westminster Bridge under Construction, Canaletto

Two arches had to be rebuilt - the picture above may well show this.
Sir Howard Douglas (in the 1840s) -

Westminster Bridge was built about the middle of the last century, under the direction of Mr. Charles Labelye.
The bottom courses of the piers were laid, or built, in floating vessels, called chests or caissons, which, when so loaded, were conducted to their proper positions, and there sunk upon the natural alluvial bed of the river properly reduced to a level, after the superincumbent mud, or other matter, had been removed; the bottoms of the chests or caissons thus forming, when the sides were taken away, the platforms or foundations of the masonry, unsustained by underpiling, or any other support than that of the gravel and sand on which they rested.
The serious defects and dangers of this mode of proceeding speedly appeared.
In the months of May and June, 1747, the western 15-foot pier of the bridge was perceived to settle very gently at first, but so much faster towards the end of July, 1747, that it was thought absolutely necessary to take off the balustrades, paving, and part of the ballast that lay over the said pier, and the two arches adjoining ; but by the continuation of the settling of this pier, those arches lost their regular semicircular figure; — considerable openings in their joints showed those arches to be in some danger ; and some of their stones, both in fronts and soffits, were split and broken — one of them actually fell out, and another was taken out to prevent its falling down.
Thus, before the bridge was completed, it became necessary to take down and rebuild two arches; and at different periods since, the whole of the structure has more or less settled or given way;

Westminster Bridge, Lord Mayor’s Day, Canaletto, 1746

The Thames at Westminster with barges, Samuel Scott, 1746

Power gives way to sail - only as the skipper of that Royal Navy vessel (flying a pennant) on the far left is possibly indicating - he will tack before running across the two sixteen oar ceremonial boats ahead of him. Is that a cloud of smoke on his port? In which case either he was demanding right of way, or possibly saluting the occupants of the rowing vessels? (Or of course maybe Samuel Scott had a good imagination!)

Westminster Bridge featured semi-octagonal turrets at intervals to provide shelter for pedestrians but they soon became haunts for cut-throats and prostitutes. Twelve nightwatchmen were hired to guard travellers.
 
1747: An early electrical experimenter was so keen to use the bridge that he did so before it was completed -

... Dr. Watson, with the assistance of the leading members of the Royal Society. A circuit was formed by a wire which extended the whole length of Westminster bridge, at a considerable height above the river : one end of this wire communicated with the outer coating of a charged phial, the other being held by a person on the opposite side of the river, who formed a communication with the water by dipping into it an iron rod held by the other hand. The circuit was completed by another person, who stood near the phial, and who likewise dipped an iron rod into the river with one hand, and was enabled, by means of a wire held in the other, to effect a contact with the knob of the phial. Whenever the discharges took place, the shocks were felt by both persons : thus proving that the electric fluid must have been in motion along the whole line of the circuit, including both the wire above and the river below.

1749: Westminster Bridge survived two earthquakes. - There were two earthquakes in London, 8 February and 8 March 1749, and they gave rise to a new explanation: (perhaps the story of Dr Watson's experiment had got about?) - anyway William Stukeley knew the answer - ELECTRICITY CAUSES EARTHQUAKES!

These earthquakes gave rise to alarmist predictions of a great earthquake which would wipe out the city. When it didn't happen there were satirical comments -

The Commissioners of Westminster-bridge have ordered this calamity to be entered in their books, as a glorious excuse for the next sinking pier.
 
The town received some comfort upon hearing that “the Inns of Court were all sunk, and several orders were given that no one should assist in bringing any one lawyer above ground.”

[ Six years later the news of the devastating 1755 Lisbon earthquake must have made the satirists wonder ... ]
 
1772: July -

On Friday Night, at Eleven o'Clock, a Butcher's Man, with his Tray on his Shoulder, was observed to stop on Westminster Bridge, from whence he threw several Joints of bad Meat into the River. A Mob soon gathered round, and it was with Difficulty the Fellow escaped alive.

1792: Picturesque Views on the River Thames by Samuel Ireland -

Westminster Bridge shown by Samuel Ireland 1792

APPROACHING Westminster, the grand assemblage of venerable and Gothic scenery, combined with the stately bridge, and other modern edifices raised within the last century, cannot fail to inspire the mind of every observer, whether native or foreigner, with an exalted idea of the wealth and splendor of the British empire.
...
... Westminster-bridge, a structure which, amidst all our boasted improvements in this species of building, we have not yet exceeded.

THIS elegant work was begun and completed from a design, and under the management, of Mr. Charles Labelye, a native of Switzerland. The first stone was laid on the 29th of January, 1739, by Henry Earl of Pembroke, a nobleman to whose skill and taste we owe much of its excellence. The whole of the superstructure is of Portland stone, except the spandrels of the arches, which are built of purbeck, a material, that is not only much cheaper, but being of a darker hue, makes a good back-ground, and gives a relief to the other parts constructed with Portland stone.

The bridge was opened for carriages seven years, nine months, and sixteen days after the laying of the first stone, and was completely finished, says the architect, in eleven years, nine months, and twenty- one days ; he likewise informs us that the whole expence did not exceed two hundred and eighteen thousand eight hundred pounds.

THIS bridge is twelve hundred and twenty-three feet in length, and its five principal arches have each more space than the width of Westminster-hall : The quantity of stone used in this building, is nearly double to that employed in St. Paul's cathedral.

IT is matter of asftonishment that we find at that period so much opposition made to the building of a stone bridge. The plan and estimate for one composed of wood was laid before the Commissioners, and favorably received but on urging the builder to fix a sum for keeping it in repair, for a certain number of years, he declined making any proposal ; notwithstanding which the wooden project had many friends, and it was only by a small majority in the House of Lords that the plan for a stone bridge was carried; those in the minority obtained the appellation of Wooden Peers.

THE utility of a bridge on this spot was urged as far back as the reign of Elizabeth [ I ]. The ferry at this place is known to have been established ever since the time of the Romans, and on digging the foundation of this bridge, was found a copper medal, well preserved; upon one side of which was the head of the Emperor Domitian, and on the reverse the figure of a woman, holding a pair of scales in her right hand, and supporting a cornucopia with her left.

AT the completion of Westminster-bridge, the advantages arising from the ferry-boat, which had from time immemorial been the property of the Archbishop of Canterbury, having ceased, the sum of two thousand two hundred and five pounds, was given to that see as an equivalent.

Westminster Bridge, 1802, Samuel Ireland

Westminster Bridge. June 30, 1792. From Surrey side.

1802: Dorothy Wordsworth wrote –

We mounted the Dover Coach at Charing Cross. It was a beautiful morning.   The City, St  Paul's, with the river and a multitude of little boats, made a most beautiful sight. The houses were not overhung with their cloud of smoke and they were spread out endlessly, yet the sun shone so brightly with such pure light that there was even something like a purity of Nature's own grand spectacles.

What a poetic diary entry! Dorothy Wordsworth might have become famous for that quotation were it not for what her brother wrote.
William Wordsworth (1770-1850) - Composed upon Westminster Bridge - September 3, 1802 -

Earth has not anything to show more fair
Dull would he be of soul who could pass by
A sight so touching in its majesty:
This City now doth like a garment wear
The beauty of the morning; silent, bare,
Ships, towers, domes, theatres, and temples lie
Open unto the fields, and to the sky;
All bright and glittering in the smokeless air.
Never did sun more beautifully steep
In his first splendour valley, rock, or hill;
Ne'er saw I, never felt, a calm so deep!
The river glideth at his own sweet will:
Dear God! the very houses seem asleep;
And all that mighty heart is lying still!

There is a 1941 version of this by F S Boas, which, after the bombs in London, sounds just a little too relevant in 2005 -

Earth has not anything to show more fair
So Wordsworth sang enraptured with the sight
Of Westminster clad in morning light
Of beauty, radiant and beyond compare;
Its towers, domes, temples glittering in the air,
And nought above them but the birds in flight.
But now the sky-borne engines of the night
Have rained their bolts with thundering and flair.
Ah! Could the singer take his stand again
Upon the bridge, how measureless his pain
To see the lovely vision maimed and marred –
But he would hear the ‘mighty heart’ still beat -
Undaunted, undismayed, and smiling greet
A Westminster whose soul could not be scarred.

View of Westminster Hall and Bridge. J. Bluck aquat. Feb 1 1810.

Westminster Bridge. W. Westall A.R.A. delt. R.G. Reeve sculpt. Published 1828 by R.Ackermann, 96 Strand, London.

1830: Westminster Bridge, published S Leigh -

Westminster Bridge, 1830

1831: The Bridge was becoming increasingly unsafe -

At different periods since [it was built] the whole of the structure has more or less settled or given way; and notwithstanding the costly works now in progress to secure the foundations from any further subsidence, and the abstraction of some thousand tons of material from the roadway, parapets, and spandrels, Westminster Bridge has again settled, and is unquestionably in a very insecure, if not in a highly perilous state. The more remote dangers of this defective mode of laying the foundations of piers, were to a certain extent kept in abeyance so long as the river remained undisturbed, in that somewhat artificial state in which it was when the bridge was constructed. But no sooner was that condition altered ; first by opening the great arch of London Bridge, then by removing the London Water-works, and ultimately by taking away old London Bridge, than all the defects of this mode of construction became very sensible, and the danger daily greater. By removing the dam which had so long obstructed the natural outfall of the River, as well as the upward passage of the tidal current, the velocity of the stream both ways has been increased, the section of the bed of the river considerably altered, while all the circumstances which constitute stability, have undergone, and are still undergoing, great modifications.
If to the removal of the obstructions, which may be considered as the main cause of these changes, there be added the construction of the embankments, such as that which extends along the river front of the Parliamentary Palace, and the numerous wharfs which protrude into the channel, diminishing its breadth and displacing vast volumes of its waters, it will be evident that not only is the velocity of the current greatly augmented, but its direction partially changed, old passages being closed and new ones formed. The sand which used to lodge on both banks is in some places nearly all gone, leaving gravel and rubbish in its place, and at other parts pestilential mud banks appear, where formerly there had been comparatively clean and deep water.
The attempt to secure the old foundations from further subsidence has been made by driving rows of sheet-piling into the blue clay round the old caissons, as a girdle, in order to prevent the materials of the natural bed of the river from being underwashed by the current, or squeezed out by the weight of the bridge into the gradually deepening water - courses ; but notwithstanding the skill and ability with which this expedient has been devised and applied by an eminent engineer, — notwithstanding the removal of between twenty and thirty thousand tons of material from the roadway, parapets, and spandrels, and even an extension of the lengths of the piers, some of these continue to sink; and it may safely be pronounced that it is beyond the resources of science or of art to render the elongated but still defective foundations capable of bearing the weight of a new superstructure, especially with an enlarged roadway.

1834: The Houses of Parliament on fire, JMW Turner. (There is another watercolour by Turner "The Burning of the House of Lords and Commons" which is far more atmospheric but with much less detail) -

The Houses of Parliament on Fire, 1830, JMW Turner.

1834: October 16th. The House of Parliament on fire, from The Gentleman's Magazine -

This evening a most lamentable event took place, which may be regarded as a national calamity, never to be forgotten. The two Houses of Parliament, with nearly all their various offices, the old Painted Chamber, associated with a thousand historical reminiscences, the libraries of the two Houses, &c- all fell a prey to a destructive fire, which broke out about half-past six o'clock in the evening.

The flames suddenly burst forth near the entrances of the two Houses, and immediately burnt with a fury almost unparalleled. In less than half an hour from the first discovery of the flames, the whole interior of the building, from the ground-floor to the roof, presented, through the numerous windows with which it was studded, one entire mass of fire. Thousands of persons instantly assembled, the engines were in attendance, the police and soldiery were on the spot, and every exertion was made to save the public papers and other important documents, vast quantities of which were conveyed to a place of safety, although many were unfortunately consumed.

All attempts to save the House of Lords proving abortive, the firemen wholly directed their attention towards the House of Commons, and to the preservation of that venerable structure, Westminster Hall, which, from the beauty of its architecture, and its close connexion with some of the most important events of our country's annals, is equally admired and estimated by the antiquary, the historian, and the citizen.

The wind, which, previous to this time, had blown from the south, ..., at near eight o'clock, veered somewhat towards the west, thus throwing the flames immediately upon the House of Commons ; the angle of which, abutting upon the House of Lords, caught fire, and, notwithstanding the utmost exertions of the firemen, assisted by the military, the roof ignited, and fell in with a tremendous crash, accompanied with an immense volume of flame and smoke, and emitting in every direction millions of sparks and flakes of fire. This appearance, combined with the sound, resembling the report of a piece of heavy ordnance, induced the assembled multitude to believe that an explosion of gunpowder had taken place.

The flames now took a different direction, but the danger to the Hall appeared to be more imminent than ever. From the House of Commons the fire appeared to retrograde as well as advance, and whilst the Speaker's house (which was partially burnt) was placed in jeopardy on the one side, the range of committee-rooms, situate immediately over the Members' entrance to the House of Commons, opposite to Henry the Seventh's Chapel, appeared to be entirely enveloped by the devouring element. A dense black column of smoke issued from the roof of this part of the building, which was almost immediately followed by a large column of flame, and the south end of the Hall was, therefore, at this time encompassed by burning edifices.

At this period several engines were introduced into the Hall, and an immense quantity of water was distributed over every part of the building. The firemen and soldiers employed on the exterior of the building also redoubled their exertions, apparently wholly regardless of the danger to which they were exposed by the falling of burning rafters and the showers of molten lead which poured down upon them on every side. Their efforts were eventually crowned with success. That venerable structure escaped comparatively uninjured ...

Ground-plan of the two Houses of Parliament and adjoining Edifices, showing the Extent of the Conflagration. 1834

1836: A ten year program to reconstruct the bridge started.

1836-1842: The 2nd, 3rd, 4th, 5th and 6th University Boat Races started upstream of Westminster Bridge.
Click Boat Race 1836-1842

1842: Westminster Bridge seen from Waterloo Bridge -

Westminster & Hungerford from Waterloo Bridge, 1842
Next to Hungerford Market a jetty protrudes into the river; Brunel's Hungerford Suspension Bridge was not built until 1844-5.
A group of boys is bathing and fishing on the unembanked foreshore below Waterloo Bridge.
Sepia and body colour drawing (215 x 4lOmm) in Museum of London (A 22150).

1854: Work started on a new wrought iron Westminster Bridge.
 
1856: A survey showed that the increased currents due to the new 1823 London Bridge had scoured away a considerable amount of sediment. Some eight feet! -

1856: The changes to the river above the 1823 London Bridge

Notice that the old Westminster Bridge impeded the water sufficiently to show the change in Low water mark either side of it. In 1823 the river was definitely fordable at low water just below the bridge. The 1737 and 1741 pictures above suggest that this might have been the case before a bridge was built here.

1862: the current bridge was opened.
748 feet long, 85 feet wide. Seven elliptical cast and wrought-iron arches supported by granite piers cross the river between the former County Hall and the Houses of Parliament. Gothic shields in the spandrels and ornamental shields emblazoned with the arms of England and Westminster provide decoration appropriate to the site. It is painted green in reference to the benches in the House of Commons (Lambeth bridge is painted red after the Lord’s benches).
Architect: Charles Barry. Engineer: Thomas Page. Contractor: Thomas Page.
It is now the oldest bridge across the Thames in London.

Westminster Bridge and the Houses of Parliament

1882: England, Picturesque and Descriptive, Joel Cook -

The Victoria Tower, Houses of Parliament, Joel Cook, 1882

1894: Plan of the Houses of Parliament -

Westminster Houses of Parliament, 1894

1884: The Colchester Earthquake (5.2 on the Richter Scale) caused three foot waves on the Thames at Westminster.
 
1890: Westminster Bridge, Francis Frith –

Westminster Bridge 1890, Francis Frith

1899: 'The Riddle of the Thames' by William Watson -

A RIDDLE OF THE THAMES

AT windows that from Westminster
Look southward to the Lollard's Tower,
She sat, my lovely friend. A blur
Of gilded mist, — ('twas morn's first hour,)-
Made vague the world : and in the gleam
Shivered the half-awakened stream.

Through tinted vapour looming large,
Ambiguous shapes obscurely rode.
She gazed where many a laden barge
Like some dim-moving saurian showed.
And 'midst them, lo! two swans appeared.
And proudly up the river steered.

Two stately swans! What did they there?
Whence came they? Whither would they go?
Think of them, — things so faultless fair, —
'Mid the black shipping down below!
On through the rose and gold they passed.
And melted in the morn at last.

Ah, can it be, that they had come
Where Thames in sullied glory flows.
Fugitive rebels, tired of some
Secluded lake's ornate repose.
Eager to taste the life that pours
Its muddier wave 'twixt mightier shores?

We ne'er shall know: our wonderment
No barren certitude shall mar.
They left behind them, as they went,
A dream than knowledge ampler far;
And from our world they sailed away
Into some visionary day.

1902: Westminster Bridge –

Westminster Bridge, 1902

1924: Some repairs were made.

Westminster Bridge © 2000 Doug Myers

Westminster Bridge going upstream

Big Ben webcam live

Map: Houses of Parliament (Big Ben), left bank

The House of Parliament and Westminster Abbey in Picturesque Views on the Thames, Samuel Ireland, 1792

Map: Westminster Abbey, left bank, behind House of Parliament

Map: St Thomas' Hospital, right bank

Florence Nightingale Museum

1610: Camden -

Saint Thomas Hospitall, re-edified, or founded rather, by the Citie of London for the sustenance of feeble and impotent persons.

St Thomas’ Hospital, Westminster Bridge and the Houses of Parliament

1837: Knickerbocker -

Last Saturday I took it into my head to go to Woolwich, nine miles from London, to help the Prince of Orange review the troops.

By dint of active exertion, I attained a seat on the deck of a bit of a steam-boat, loaded with two hundred and fifty pleasure-seeking mortals like myself, while as many more were left disconsolate on the wharf— inadmissible.

Off we went with the tide, under Westminster, Waterloo, Blackfriars, Southwark, and London Bridges, over Thames Tunnel, and between a multitude of ships and steamboats, large boats and small boats, rowed perhaps by a Jacob Faithful, or his posterity, and following the serpentine course of ' Old Father Thames' through a beautiful green meadow, passed Greenwich, and arrived at our ultimatum in good time to see the show.

The prince was dressed as a general, decorated with half-a-dozen badges of different orders; and he galloped about the field in true military style, accompanied by his two sons, and a squadron of princes, dukes, lords, etc.

They fired bombs, and had a grand imitation-battle, with horse-artillery — in other words, a sham-fight, which was all vastly fine.

Charles Dickens, Sketches by Boz, Chapter 10, The River –

This is the most amusing time to observe a regular Sunday water-party. There has evidently been up to this period no inconsiderable degree of boasting on everybody's part relative to his knowledge of navigation; the sight of the water rapidly cools their courage, and the air of self-denial with which each of them insists on somebody else's taking an oar, is perfectly delightful. At length, after a great deal of changing and fidgeting, consequent upon the election of a stroke-oar: the inability of one gentleman to pull on this side, of another to pull on that, and of a third to pull at all, the boat's crew are seated.
'Shove her off!' cries the cockswain, who looks as easy and comfortable as if he were steering in the Bay of Biscay. The order is obeyed; the boat is immediately turned completely round, and proceeds towards Westminster-bridge, amidst such a splashing and struggling as never was seen before, except when the Royal George went down.
'Back wa'ater, sir,' shouts Dando, [the boatman]
'Back wa'ater, you sir, aft;' upon which everybody thinking he must be the individual referred to, they all back water, and back comes the boat, stern first, to the spot whence it started.
'Back water, you sir, aft; pull round, you sir, for'ad, can't you?' shouts Dando, in a frenzy of excitement.
'Pull round, Tom, can't you?' re-echoes one of the party.
'Tom an't for'ad,' replies another.
'Yes, he is,' cries a third; and the unfortunate young man, at the imminent risk of breaking a blood-vessel, pulls and pulls, until the head of the boat fairly lies in the direction of Vauxhall-bridge.
'That's right - now pull all on you!' shouts Dando again, adding, in an under-tone, to somebody by him,
'Blowed if hever I see sich a set of muffs!' and away jogs the boat in a zigzag direction, every one of the six oars dipping into the water at a different time.

1839: Rowing Match -

The grand scullers' wager, for a purse of sovereigns, given by the amateurs, took place on Thursday. The whole of the competitors were picked from the best on the river, and large sums of money depended on the result. The distance was from Westminster Bridge to Putney, with tide, and seven scullers were to contend for the golden prize, whose names are as follow: H. Barrow (Blackfriars), scarlet; Ivy Noulton (Lambeth), black; H. Norris (Hungerford), light blue; G. Maynard (Lambeth), green; T. Loader (Bankside), orange; J. Parish (Strand lane), white; C. Campbell (Westminster), stripe.
The start was very good, but Norris might have been quicker. Campbell and Parish were close up with Norris rather in the rear; Parish, however, lost his place in a few seconds, and Campbell and Norris, as first and second, kept their positions the whole of the way. Campbell only won by a few lengths.
 
On Friday ten gentlemen, belonging to the Guards, contended in a sculler's match, from Westminster bridge to the Red House, for a sweepstakes. The start took place about half-past three o'clock, and, after an excellent match, Captain Douglas came in first, followed by Captains Stanley and Dixon. The remaining seven shortly after arrived at the stipulated distance.
Viscount Chetwynd started the men. The match was under the management of R. Wright, coxswain to the Guard's boat.