Have you considered using Airbnb? I have the app on my phone -it's pretty useful for finding somewhere to stay that's cheap.
I used in when i went to NY, they have some places in London too but less choice I guess. But you can find under £100
Otherwise Google has a good comparison tool you can find rooms with here.My advice is to skip the mega-cheap ones and also look at where they are on the map. Some of them are miles away from anything.
The more you can afford to spend, the better it gets - and if something looks too good to be true it probably is.