Castle Weir Stream

Immediately above Osney Footbridge, on the RIGHT bank (your right as you go upstream) is the Old Oxford Navigation, Castle Weir Stream, which can be followed up to a weir. It rapidly gets shallower and swifter. It is the outflow from Castle Mill.
The other side of this weir can be approached by leaving the main river at Four Rivers. Old Oxford Navigation.
Punts and Canoes only - and it really doesn't get anywhere!

This section in The Stripling Thames by Fred Thacker

Fred Thacker's Map, 1920
Fred Thacker's Map, 1920.

1909: The Stripling Thames, Fred Thacker -

Just past this first bridge [Gasworks Bridge now Osney Footbridge] you will see on the RIGHT bank a triangular grassy island, called in the old maps George Island.
The stream that enters on its eastern side is the ancient main navigation from Medley Weir.

Weir Stream Footbridge -

Footbridge over Oxford weir stream
Footbridge over weir stream, seen from upstream.

Oxpens Bridge, the A420

Oxpens Bridge
Oxpens Bridge, weir stream.

The approach to the bridge has some large stones which grounded the punt - but I got through. Above was a shallow stream which did take a little negotiating.

Weir stream Walkway

Walkway over Oxford weir stream
Walkway over weir stream

Stream splits, the right bank stream was too shallow and full of rubbish.
On the RIGHT bank stream a wooden Bridge -

Wooden Bridge on Oxford weir stream
Wooden Bridge on weir stream.

A few yards above this a line of stones across the stream ended my explorations 50 yards short of the weir by Oxford Castle.
The other side of the weir can be reached via Four Rivers and the Old Navigation.