Rick Steves list this hostel in his book and on this site. It is in Notting Hill:
$ Norwegian YWCA(Norsk K.F.U.K.) is for women under 30 only (and men under 30 with Norwegian passports). Located on a quiet, stately street, it offers non-smoking rooms, a study, TV room, piano lounge, and an open-face Norwegian ambience. They have mostly quads, so those willing to share with strangers are most likely to get a bed (July–Aug: Ss-£32, shared double-£30/bed, shared triple-£25/bed, shared quad-£21/bed, includes breakfast and sack lunch; Sept–June: same prices also include dinner; 52 Holland Park, tel. 020/7727-9897, fax 020/7727-8718, www.kfuk.dial.pipex.com, [email protected]). With each visit, I wonder which is easier to get — a sex change or a Norwegian passport?
The Oxford Hotel (http://www.oxfordhotellondon.co.uk) is an option. Its actually in Bayswater and close to Kensington Gardens. Its also close to a stop for the double decker bus tours. Its quite affordable, comes with a continental (as opposed to English) breakfast, and has microwaves and refrigerators in all of the rooms.
The London Vicarage Hotel is more expensive than the Oxford, but its in the area you'd like. It's a great place.
There are more hotels listed in Rick Steves' guidebook as well.