There is not such thing as a cheap hotel in London. Hell people come on holiday and stay in hotels in Croydon of all places because of the cost of London hotels, and they ain't really cheap here either.
What's your budget?
I'm struggling to find anything that cheap, what area of London do you need to be in.
If you have a spare £4000 a night for a room, try the Lanesborough Hotel. You get a chauffeur-driven Bentley for your exclusive use for the entire duration of your stay and your own butler.