Since your onward flight doesn't leave until the evening...

try http://www.ryanairhotels.com/live/sp...ers/london.htm

I saw a room listed for one person on the 08 Sep listed for £25.

I'd say Highgate (the place mentioned) was a little over 2 hours from Heathrow using the Tube (it's on the Northern line).
There was also a room for £45 at Finsbury Park which is about 1.5 hours direct on the Piccaddily line.