Hotels in London are not cheap ..not even the ones called 'cheap'. There is no middle ground in London. Either you are at an expensive but really good hotel or a crappy hotel. They haven't exploited the middle ground market and it going to bite us in the ass for the Olympics.
NEVER stay in an inner city London B&B at that sort of price..it *is* going to be a crappy place that you share with the recently not homeless.
If you don't care about fancy stuff, find a travelodge -
http://www.travelodge.co.uk/ ..there are a couple in the Soho/Covent Garden area which are clean and safe and not expensive by London terms.