This bridge carried Cox's Walk over the railway line which ran from Nunhead to Crystal Palace High Level station. The railway closed in 1954 but over half a century later, the footbridge is maintained in good condition.
A board, just visible in this image, on the parapet of the bridge confirms that it was from this bridge that, in 1871 Camille Pissarro painted his famous view of Lordship Lane Railway Station.
Link
To see how the bridge looked when the railway line was intact, and in the intervening years as nature has gradually reclaimed the site, have a look at the Disused Stations website
Link . The second image on that page is very close to Pissarro's view.
See also
TQ3472 : Bridge over dismantled railway, SE26.