Dover St Bar on Gt Dover St has rooms at £10/night or £60/week per person at the moment. I've not tried it but have heard it is quite good.
Failing that I have heard that the London School of Economics has lots of unused accomodation on Bankside. I've done a quick websearch and come up with the following ..
The London School of Economics
Offers reasonably priced accommodation at six different locations in the city.
- 24 Sumner Street
, SE1 9JA, Tel: 020 7633 9877, Fax: 020 7574 6730, E-mail: firstname.lastname@example.org