Best thing to do for a cheap hotel is use a site like laterooms.com or activehotels.com ...they have reviews and photos, as well as discounted deals. Check out whether or not breakfast is included and if so, whether it's a "continental" breakfast which is often just cornflakes and half a croissant (husband has just been accommodated in a cheap place near Victoria where this was the case - this was booked for him, much to my annoyance as I know I could have done better!). Not a problem if there's no breakfast, but it's good to know - cheap breakfasts can be had from all manner of department stores, shops, Wetherspoons and Subway. If you stay at a Holiday Inn Express a better version of the continental kind is free, and if you stay at an Ibis (reliable chain) you pay for a very copious buffet breakfast, which is worth doing.
We have generally found good hotels (not as described above by Leeneia)through laterooms and activehotels for the kind of money you're talking about. Don't be put off if the hotel is out of the centre of London as public transport is easy. There's an Ibis, for example, at ExCel (the exhibitions centre in Docklands) where you can be very comfortable and within easy reach of everything using the Docklands Light Railway.

Anne