I've noticed these bridges in the past and whilst they seem vaguely intact, they do still look very decrepit and it's certainly surprising to think of more capacity on this stretch of line, which today operates with reasonable success!
The depot and sidings currently take up a lot of the space that the Down Streatham Hill Relief (or whatever it was going to be called) line would have, and of course there is a third platform at Streatham Hill which is strictly for empty stock and emergency use on the other side, as well as various pointwork and the arrival/departure routes. All in all, I can't see there being any need for running lines over those bridges in this day and age.
Both Bridges have another 3 tracks of unused decks on the down side. (So 6/7 track to Streatham Hill!). My suspicion was that it was done to so that the down sidings (originally coal sidings) were accessible from the Balham end and that there was much greater siding length available (when converted to passenger use?). If so this might align with the pre WW1 vintage works that included rebuilding Clapham Junction to give the current Southern setup. This might be where the works stopped due to WW1?
There also used to be 4 platforms at Streatham Hill. The short lived 4th platform was a bay on the down side. The track to this platform apparently aligned with the current sandpit beyond the trap points at the entry/exit to the down sidings.
Also worth noting the remains of the OHLE masts beside the down line. (LBSCR AC electrified 12th May 1911 to 1929? on this route).
1913 (survey date) OS
http://maps.nls.uk/view/103313420
Western Bridge 3 track (1 up siding, 2 running lines)
Eastern Bridge 4 track (2 up siding, 2 running lines)
No sign of extra bridge decks or retaining wall
1949 OS
http://maps.nls.uk/view/103029897
Western Bridge Potential 6 track (1 Up sidings, 2 running lines, 3 unused decks on down side)
Eastern Bridge Potential 7 track (2 Up sidings, 2 running lines, 3 unused decks on down side)
Effectively as at present
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Addendum:
LBSCR decided in 1920 to electrify all the way to the Coast but this was cancelled on grouping in 1922 so maybe the plan was to have a large set of EMU sidings at Streatham Hill?