I will go to London again as well in August so I have done a search myself. Been to there 3-4 times beforel
You may check these out that I have short-listed before with price online shown as well
St Giles Hotel & Leisure Club Bedford Avenue, WC1B 3GH London 81pounds
Bonnington Hotel 92 Southampton Row, Bloomsbury, Camden 116pounds
Radisson Edwardian Grafton Hotel 130 Tottenham Court Road, Camden 118pounds
Novotel Hotel Waterloo 113 Lambeth Rd, SE1 7LS London 130pounds
Melia White House Hotel Albany Street, NW1 3UP London 112pounds
check the lodon map here http://www.ukguide.org/london/londonmap.html
Those names shown closest to the centre is the heart - Piccadilly circus, Tottenham Court, Covent Garden, Oxford Circus, Leicester Square, Holborn are the town centre where a lot of sites and museums are close by or very accessible by subway.
Wish you have a good stay there