Depends what you're after I suppose, just a room or a flat? Fulham/Chelsea is one of the nicest areas in London so is probably going to be expensive, although I've never looked. Probably cheaper a bit further out like Hammersmith, Acton, Brentford etc. Even if you went right out to Uxbridge/Hillingdon Stamford Bridge and central London are easy to get to so don't worry about that.