If you're south, there's the Arch for bouldering, but if you want some proper walls I'd highly recommend the Reach in Woolwich. Loadsa walls, pretty big bouldering area too, good cafe. Getting there is easy enough with a bike, or Charlton station is pretty close. They also have one night a week where you can go and climb with a load of other people who can't find a climbing partner so you can get a belayer, can't remember which day though...
If you're south, there's the Arch for bouldering, but if you want some proper walls I'd highly recommend the Reach in Woolwich. Loadsa walls, pretty big bouldering area too, good cafe. Getting there is easy enough with a bike, or Charlton station is pretty close. They also have one night a week where you can go and climb with a load of other people who can't find a climbing partner so you can get a belayer, can't remember which day though...