In the past it has been hard finding a hotel that will let 4 people stay in a room. Should we stay outside London and travel into the city. Where? Thanks for any suggestions!
Err, just be aware that the OIympic period over summer will be really busy and expensive (the Games open on 27 July and go through until mid-August).
Aside from that, why don't you try booking hostels that have 4 bed dorms? Or try and book 'Family rooms' which usually have a queen and 2 singles. Nearly all other room types are singles, doubles or twins and won't fit 4 people.
The other option is to look for apartments, maybe a 2 bedroom one would suit - try http://www.airbnb.com/ about 8 years ago