Balham
If it ain't in London then, well, it just ain't.
The station opened in 1866 (gosh, when Brixton was still in Surrey!). The South London Line was er. . .authorised (?) in 1862. So, where would the bridge go to? At present the abutment is opposite Brixton station road so a bridge would have gone nowhere, apart from hoovering above Brixton Station Road. A map of 1894 is all I can find for the present. c(after some more searching . . .) I have found a map of 1876. This shows that Brixton Station Road does not go all the way through to Barrington Road. It might have turned north at Canterbury Crescent, not traversing Gresham Road norgoing as far as Barrington Road (as it does today). Oh, the map . Best to enlarge it and compare with a modern map but East Brixton Station is there. The orphanage (hence Orphans Yard) opened in 1876 but does not say when it was built.Was there a bridge or is that just a retaining wall?
As an aside, for those that want to go further back, here's a map from 1824.