In reply to Euan Todd:
no brainer go to Bristol. I've lived in both...
London is a complete nightmare if you want to outdoor climb, its generally a long drive with crazy traffic. I'm actually born in London (until age 15) however as an adult I found it too much. Its dirty, busy, urban and impersonal.
Bristol is a vibrant city with lots going on. The surrounding countryside is nice too.
There is reasonable climbing inside the city on limestone at the Avon Gorge and lots within a short drive. Further afield a 2.5 hours drive gets you to Pembroke and or Cornwall both of which host some of the best sea cliff climbing in the UK. Its also only a couple of hours to Portland the best sport climbing destination in the UK. The western peak district is also only 2.5 hours a way.
It is quite poorly connected for mountain climbing, but for walking / running / biking you have the area around the black mountains which isn't far.
Dartmoor whilst not mountainous does have a nice feel to it and is under two hours away, with a lot of bouldering and mostly shorter routes.
Post edited at 19:00