Just got back from London. During my trip my cell phone I used from a previous trip broke. In London I popped into a cell phone company and got a new one for 20 pounds. They made me add 20 pounds worth of airtime but I was able to transfer my previous balance from my "broken" phone to the new one by calling customer service.
So for those who are contemplating about getting a cellphone in London (or for any part of Europe) just get it when you get there. The pay as you go is so easy to get... and not expensive either!