London has thousands of hotels, with a huge variety of prices. Generally speaking the closer you want to be to the cnetre of London or overlooking busy tourist spots the more you’d have to pay.
As with many things in London the earlier you book the more you can save. The hotel chain Travelodge for example offers rooms as cheap as £9 a night if you manage to catch one of their special offers. But generally speaking most of their rooms start off at £29 per night.