I've lived in London in flats for 4 years - but am travelling at the moment. When I return, I'll need some accommodation for 2-4 weeks - just short term. Hostels are one option, but they're per night, dorms etc - if there's some cheapish short-term accommodation with a private room, that would be perfect. Will have had enough of dorms after 3.5 months backpacking ;)
Airbnb worked a treat for us in London, there's plenty of choice in all price brackets. (No affiliation, just a happy customer.)
In addition to the sites already mentioned, you may have some luck with Craigslist's London rooms section also.