The main mouth of the Cherwell is an artificial cut on the RIGHT (east) bank above (north of) Donnington Road Bridge.
Left and Right banks are now identified as going UPSTREAM (Environment Agency decision)

Do not be mislead by the word "Cut" - this is not a canal cutting and is not suitable for powered boats. It was cut to relieve flooding in the Christchurch meadows bypassing the tortuous old mouths of the Cherwell

The first mouth is the twisty old stream which reaches the Isis further upstream, the other side of the row of ten boat houses.
The (now blocked - and now third mouth) is otherwise called Shire Lake Ditch and reaches the Isis downstream at Freshman's River.

OS map showing mouths of Cherwell before new cut was made (actually published 1896:

Map Cherwell Mouths before new Cut, published 1896
Map of Cherwell Mouths before the new Cut, published 1896

1884: Construction of the new Cherwell Cut, Henry Taunt -

Construction of Cherwell Cut, Henry Taunt, 1884
Construction of Cherwell Cut, Henry Taunt, 1884
© Oxfordshire County Council Photographic Archive; HT02723

As you laze along this beautiful tree lined section, give a thought to the labourers who dug it out by hand! The photo shows no trees at all here in 1884. We have to admit that nature has done a pretty good job on the banks of this new cut.
The RIGHT, east, bank is part of Aston's Eyot Nature Reserve.
The whole river from Cricklade to Teddington (and of course beyond in both directions) is very much an artificial creation. Nature re-asserts itself and adapts - but essentially the river is a work of art. It was shaped by monks and millers and bargemen, by the requirements of their monasteries and water wheels and weirs and towpaths.
And now all that has gone and what remains is the water supply for London, and the boating leisure industry, together of course with the river activities - fishing and rowing and sailing and punting and walking. Fortunately all these together have been able to attract enough money to keep the Thames in excellent condition from the boaters' point of view!
Our thanks to those who help to maintain it so well.
Long may it be so - Where Thames [ and Isis and Cherwell ] Smooth Waters Glide. John Eade

1953: Oxford by James Morris -

When the Thames is half-way to its mouth the River Cherwell joins it from the north, at a point where the counties of Oxfordshire, Berkshire and Buckinghamshire more or less meet.
This is the very middle of Middle England, almost as far from the sea as you can be in these islands.
It is pleasant country, but mouldy, as though the damp has got in.
Once heavily forested, now it is mostly meadow land, interspersed with low wooded hills and threaded by the flood, fields, soggy but fertile, that line the rivers themselves.
Its villages, by and large, win no prizes from tourist associations; Its country houses, though fine, are often in bad repair, standing as they do just outside the fructifying range of London's commuters.
Its rectories have often been sold to the laity, and are decorously done up by local solicitors, or camped in by blithe Bohemians with uncountable children.
There is nothing spectacular to this stretch of countryno downland above the river, no magnificent gorge, not even a white chalk horse on a hill face.
It is standard England rural scenery: just, as exiles from London like to say with a sniff just country.
The junction of Thames and Cherwell is equidistant from the three main sea inlets of southern England Thames Estuary, Bristol Channel, Solent.
If you plonked a cross on a map of the southern country, its arms would meet somewhere here.
The site is thus almost allegorically central, and is an ancient and important crossroads.
Here the main road from Birmingham to the south coast crosses the Thames, at a point where the shallow gravel bottom has always made an easy ford.
A mile or two away a big lateral road passes on its way from London to South Wales.
The railway from London to Gloucester runs nearby, and westward come the trains from the iron-fields of the upper Midlands, taking ore to the Welsh steel mills.
Here, too, the Thames is linked with the English canal system, spreading fan-like through the Black Country into Yorkshire.
Five bridges cross the Thames at this place, and in the winter most of those condescending old pleasure steamers come here to hibernate.
It is a fulcrum: a hub where the industrial energies of England, rampaging across this pastoral country from factories to ports, distributors to markets, meet with a roar of exhausts in an environment of moist green languor.
Around the crossroads stands the middle-sized city of Oxford. ... Few cities have been more loved, loathed and celebrated.