Hostels have in my experience (which in the last few months has become quite a lot, lol) been at least as comfortable, if not more so than cheap hotels.
http://www.hostels.com/london is a good place to look (hostelworld.com is better, but it seems to be down at the moment) If you have a group, you can hire an entire room out yourself, as well.
I've stayed at the Journey's chain in London twice - they're simple but perfectly adequate, and located near to tube stations - I've stayed at the one in Kenington, which is about a 5 minute walk from Kennington Tube, and the one at Edgeware Road, which is right next to the tube station. Both are located above pubs, but they're not loud, or anything. They're about 15 pound a night, or a little less.
There's also St Christopher's Inns, which are more cheerful (I stayed at the Hammersmith one, and also the one in Bruges):
http://www.st-christophers.co.uk/london-hostels Again, they're near the tube stations, so it hardly takes any time at all to get to anywhere. They're also about 15 pound a night, though it may vary depending on the location - there's 7 of them in London, and they're located all over the city, depending on where you want to be.
*cough* I think I spent too much time in London when I was backpacking
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