It's not VERY old. According to this page
https://thames.me.uk/s01530.htm the current structure is the third bridge on the site, built in 1929. There are short brick-built viaduct sections on land at both sides of the river, the one at the south end being the longer one. From the photo up-thread, the curve suggests the problem is with the south bank support for the southerly steel span. I wonder if its foundation has been scoured out by recent floodwater?
That date of 1929 on thames.me.uk has got onto the wrong page - it relates to Appleford viaduct. The bit about "a single bow structure" clearly belongs there.
If you rely on the two pages of the Great Western Railway Magazine, quoted by Culham Ticket Office (
Nuneham and
Appleford), and on some news reports from 1931, you get this sequence:
The first steel bridges at Nuneham and Appleford date from 1856, were very similar, and each extended as a viaduct - to the north (Nuneham) or both ends (Appleford).
The bridge part at Nuneham was replaced in 1906/7 with the current two-span structure. The viaduct part was kept (but perhaps shortened a little). New piers were built mid-river and on the north side; I have no information on what was done to the southern abutment. It must have had new bearings, perhaps allowing for expansion; on the north pier the girders appear to just sit on blocks of concrete.
Appleford was all replaced in 1927/29, with a single-span bridge and brick arches. This bridge had "roller bearings". The new bridge is slightly to the east of the old one, so that two tracks could be kept open throughout the work.
The viaduct part at Nuneham was rebuilt in brick (finishing) in 1930, following the pattern used at Appleford.