The Old River, the natural course, Right bank, avoiding Desborough Cut is very lovely and navigable for most boats (if not all?)

Desborough Island -

South East quarter is Waterworks, reservoir and pumping station
North East quarter is Sports Ground with Clubhouse
South West is Sports Ground adjacent to waterworks
Remainder is rough field

1758: A Description of The Thames, Binnell & Griffiths

SHEPPERTON is a Place of no great Account, unless for being much frequented in the Summer Season, by those who are Lovers of Angling.

Shepperton 1752

1901: The Thames Illustrated by John Leland

More than a dozen times between Walton and chertsey, which, as the crow flies, is a distance of but three miles, does the wayward and varied Thames turn, now to the right and now to the left, in great sweeping curves that are often contained within a right angle.
Infinitely diversified are the prospects as the noble stream sweeps between Halliford and Shepperton on the Middlesex bank and Weybridge on the other. The wooded slope of old Oatlands Park, the fur clad heights of St George's Hill, the beautiful meadows by the tributary Wey, the green and shadowy lanes, and the noble river contribute to make a series of most delightful pictures.

Site of Halliford Bridge ???

1937: "The Thames and its Story" has this statement -

Halliford Bridge was washed away some years ago by the floods; and now, about half a mile below Halliford, the Surrey and Middlesex shores are connected by a brick and iron structure which is named Walton Bridge.

Anybody know how to sort this out? The pictures of the second Walton Bridge appear to show another bridge to the north west of the Walton Bridge. Was this Halliford Bridge? Did it bridge what was then the main channel?
British History Online - Hundred of Spelthorne says:

The Thames has changed its course at Shepperton, causing anomalies in the boundaries of the parish and county.
At Walton Bridge the boundary follows a minor stream so that the meadow called Cowey on the south bank lies in Shepperton and in Middlesex. Another small bit of the south bank farther west is also in the parish for the same reason. Both were considered by the parish officers in the 19th century to lie in Surrey, while in 1847 the parish unsuccessfully claimed six acres in Weybridge Mead [now Desborough Island].
On the north bank many of the fields were surrounded by ditches of running water and were described as aits, and there are references to erosion by the river at several times: money was left to the water defences of Shepperton in 1504, the old church seems to have been destroyed or rendered unsafe by encroachment of the river about the end of the 16th century, land near Walton Ferry was said in 1633 to have been washed away, and the loss of 20 acres in Halliford manor between 1650 and 1739 was attributed to erosion.
Elias Ashmole (1617-92) associated the cutting off of Cowey from Middlesex with the destruction of 'a church', presumably that of Shepperton, which he told John Aubrey had been swallowed by the waves.
Breaches in the banks at Stadbury (Hamhaugh Island) were repaired in the 18th century by the city of London authorities, who were responsible for this stretch of the river. They also had occasion to remove illegal fish-weirs: there had been a weir at Shepperton in 1086 and one is mentioned in the 14th century. The stakes found in the river at Cowey and popularly connected with Caesar's crossing of the Thames are very likely to have been the remains of one of the former weirs.

Halliford

Right bank at the most northern point of the eastern, downstream excursions of the river.
The Thames Illustrated, John Leland, 1901 says

Halliford, a pleasant village, whose name is supposed, though doubtfully, to preserve the memory of the great ford across the Thames

Lantern Slide (1883-1908) - Shepperton
Pictures by W.C.Hughes. Thanks to Pat Furley, research by Dr Wilson.

Gibbs Marina

Right bank at the point furthest north on the old course
1996: The chandlery here was burnt down. There have been various planning applications. I am uncertain of the current position.

Sailing Club

Right bank above Gibbs Marina

Shepperton

Right bank at the northern point of the upstream excursion of the river.
The Thames Illustrated, John Leland, 1901 says

Shepperton is a delightfully quaint place still, with fine houses standing amid trees, a green framed with chestnuts and elms, and a pretty surrounding country. ...
The Church looks charming from the water, but has been a great deal altered since it was built in the 16th century, to replace an earlier structure which stood in the river on piles.