No such thing as a cheap studio in London.
If you prefer digital or if you don't care if it's recorded on either tape or 'pooter then Onecat studios in Brixton is unreasonably cheap and of a very high quality. Jon, who runs the studio, is a very talented musician and is a great listener both in terms of understanding what the client wants and a musical ear. He has recorded a lot of commercially acclaimed UK artists including Chris T-T, The Speed Of Sound and Scarlett's Well (ex-Monochrome Set). He is also responsible for the recording of the new Manic Cough single that is currently doing the rounds on Radio 1.
http://www.onecat.co.uk/
http://www.myspace.com/onecatstudio
There are some things to listen to on the myspace site.
If it's that tape machine and 3rd harmonic distorition stuff you are after, then the Fortress in Old Street is the cheapest I know of. We used it with Steve Albini to record our album last year and it sounds ace.
http://www.fortressstudios.co.uk/
We used it for our album. The desk went on fire a bit but generally good for the money.
Otherwise Southern Studios is quite competative.