In reply to th1nk:
London is not very near to the climbing in the UK:
http://www.ukclimbing.com/logbook/map/
Most climbing in the UK is not bolted. The nearest climbing that is bolted is Portland, which is about 3 hours drive away.
Your best bet is to try and meet up with other London climbers, and share lifts if at all possible.
There are several climbing walls in London - where abouts will you be staying? London is a massive city and it can take a long time to travel from one part of it to another.
It's worth trying to sample some of the other climbing in the UK, so meeting other climbers will allow you to do this. I would recommend Snowdonia, Cornwall, the lake district and the Peak, but all of them really need you to go there for a weekend at least from London and can be hard work without a car.
There are several London based climbing clubs too, that might help you hook up with local climbers:
https://www.thebmc.co.uk/map
Good luck and have fun!