I've gleaned some more information from somebody who was in contact with railway staff via another forum, and the pieces of the different reports are now falling into place a little better.

Vauxhall station is elevated on a bridge structure over the roads below, so there are parapets and at one point a high wall immediately behind the track for platform 1. You can just about see it on the Google satellite imaging if you zoom in -- platform/track 1 is the one on the far left.

Apparently the man was seen on CCTV walking off the end of platform 1/2, then crossed track 1 to get to the side wall, so that he was then on the third-rail side of the track. He then disappeared from view into the one the refuges in the parapets intended for permanent-way workers. That's where the newspaper reports have gotten the "recess" business from.

This is the view looking south along platform 1, although I didn't get whether he walked off the north or south end of the platform, but it gives an idea of the layout and structure:

http://www.geograph.org.uk/photo/614524

The northern end of platform/track 1 can be seen less clearly the last link of my previous post.