The bridge was, as explained elsewhere, widened at some point to allow the river to run under the marshalling yard site. It would appear that it flows under the former west end reception sidings location. When there was a yard, it connected to the Down and Up Windsor just before the road bridge, with a shunting neck. Sometimes a diesel shunter would be parked on the dead-end neck up against the road bridge, as I think there was a staff canteen or club the opposite side of the tracks at ground level, which later became a signalling HQ.
I live in Feltham and am sitting about half a mile from where it's all happening- or not- so hope I can fill in some of the gaps, a bit quicker at any rate than it looks like the track re-alignment will take. Original estimate was Friday; now Monday is being publicised, but I think even that's probably a bit optimistic, especially if there's further heavy rain.
The original bridge across the River Crane did adjoin the marshalling yards- ironically, of course, presently the object of BAA's attentions as a potential site for the Airtrack depot or even a possible future tie-up with SWT. It will be interesting to see how this incident affects those plans actually- at the very least, it's bound to delay them.
However, the marshalling yards closed in 69 but NR still own the freehold on the land- one of the reasons why it's a relatively straightforward matter to clear the adjoining land for slewed track over the Crane Culvert. Less straightforward perhaps is that there is also a pedestrian tunnel under the line, also poorly maintained but widely used by dog walkers and locals. NR, Hounslow Council and others have been arguing for years about who should pay for the lighting through it.
Another factor that may have played a part, though, is that the course of the river was diverted in the late nineties when Royal Mail took over part of the land ( I don't know whether they hold the freehold) of the marshalling yards for the Jubilee Mail Centre. A smaller, separate bridge was built at this point to carry the roadway through Godfrey Way to the mail centre, but I can't recall, momentarily, whether there is also a rail bridge there.
I suppose it could have been worse- at least the bridge and the river are west of Feltham junction, just.
The club referred to is still there- formerly the ASLEF club, it's now called the Feltham railway club, I think and is indeed at part of the Marshalling yards site. The 70s signalling cen,tre, which replaced Feltham West is located just to the east of Feltham station on the up line. By the way, it is the up-line, i.e. north, side of the bridge, where the worst damage occurred. It's also a small mercy that there is still bi-directional working through Feltham.
Hope this helps to clarify some points. My only claim to industry knowledge is that my grandfather was a South Western division EMU driver based at Strawberry Hill until his retirement in the late sixties, but maybe the local knowledge will be of interest to forum users.