I would echo Bonzo's suggestion and put a topic on the UK boards, there are a lot of people that will try to help you. If you do a little research you'll find a few topics on there that have asked these questions before.
I would look into something like Expedia to get a decent deal, June is quite a nice time of year to visit London, but even so there will be plenty of competition from the hotels for your business. You should get some good deals. I would suggest staying reasonably near the centre of London, IMHO staying out near the airport would cost more in train fares ($25-30 per person per day) to get in and out of London that you'd be saving in room costs and you'd be spending 2-3 hours travelling each day.
Things to do when you're there . Tower of London, Buckingham Palace, London Eye, Jack the Ripper walk, Hampton Court Palace. I think the Chelsea flower show may be around that time of year ( there's also one at Hampton Court Palace), Covent Garden, Tower Bridge, Houses of Parliament, St Paul's Cathederal and Westminster Abbey