Morley College in Westminster Bridge Road has an extensive range of classes for all levels from beginner onwards. Any class in their prospectus (available online) taught by Wendy Metcalf or Craig Snelling will be hard work but brilliant and good value for money.
Wendy Metcalf also does her own workshop classes and usually holds them somewhere in SE1 -- I've been to some she's held at St Jude's Community Centre, near the Imperial War Museum, which have been excellent. Don't have the details right now but could find them and ask her if I can post them on here.
If you're interested in getting involved in productions / play readings, there are also some local theatre groups - Network Theatre under Waterloo station (www.networktheatre.org) and South London Theatre, although that's a bit further away in West Norwood but trainable from London Bridge or bussable from Elephant and Castle / Waterloo (www.southlondontheatre.co.uk). I think Network are doing a play reading this Sunday...
Morley classes are very good too - Wendy Metcalf and Craig Snelling are indeed very good teachers but I have also had classes there with Ann Garrett and Olusola Oyeloye who are also very good. Morley college also run an excellent course in partnership with The Globe theatre, called Groundlings on Stage, where you get the chance to work with Masters from the Globe and education staff, and do an ensemble performance on the Globe stage. The Globe run a number of education events throughout the year, including Sam's Weekend (celebrates Sam Wanamaker's birthday) where all events are free and last year verse and movement workshops were offered along with lectures on Shakespeare in film and stage combat demonstrations.
There are also a range of classes at City Lit (www.citylit.ac.uk), which I've heard good things about.