Alot of people here are saying you can get cheap rent in London if you're willing to travel in from the suburbs. Yes this is true. But it is also true that transport can be very expensive. You can easily spend £20-£30 for a return train ticket which would cost you £400 to £600 per month in travel costs. So be careful about choosing where you live. At that rate it may be better to live at walking distance to office.
My advice is to live South of the Thames (generally cheaper) and then commute in at about £10-£15 per day. Still £200 to £300 per month. It's quick too.
LOndon is awful for cycling also. I hear Berlin is very cycle friendly. So you could save alot in Berlin on rent and transport.