bouldering at the Arch at London Bridge, bouldering at Mile End in east london, and sport and bouldering at the Castle in north london...there are others but not as good.
and obviously the westway - the best (by a very big margin) for routes and very good (and much less crowded than the rest) for boulders too, plus they've got a ping pong table, good for warming down:)
How to get into a british climbing gym: http://www.youtube.com/watch?v=u2zg23N5zXY Well itยดs not London, but you could try and report whether it works after your return.
Climbing gym in London