This link, from the Greater London Authority (based on data from the Valuation Office Agency, so it should be authoritative) will help you see the level of rents in different areas:
http://www.london.gov.uk/rents/
Remember that living just outside London often isn't much cheaper than living within the city itself (because so many people commute in daily). Indeed, living in some areas just outside of London (such as the fashionable towns to the south-west of the city) can cost substantially
more than living in the city. Things only start getting (a bit) cheaper when you live over an hour from central London (with the obvious downside of much higher rail fares) unless you're prepared to live in a grotty area, such as Grays (which is convenient for London, with surprisingly cheap accommodation but is a total dump).