Hi Amna, welcome to the UK.
Some reasonable advice so far but probably not all of it helpful if you don't know much about climbing in the UK.
The Climbers' Club website that 999thAndy posted - that shows a few climbing areas, but only the ones where the Climbers' Club publishes guides! There are *lots* more areas. Of most interest to you, it misses of the entire Peak District.
You have been advised to visit the sandstone near London, and you've been advised not to visit it! Not hugely helpful. It's the closest climbing to London. I've never climbed there, but I get the impression it's not brilliant. It is, however, a lot closer than the Peak District.
For sport climbing, you could look at Portland. There's a new guidebook just been published.
http://www.rockfax.com/climbing-guides/books/dorset-2011/