Hi, I stayed in London for the Olympics and I stayed in a service apartment that was big and spacious. Felt just like living in my own home! Use online booking to book. I stayed in the Hammersmith area which was accessible everywhere and very convenient from the airport without having to slug heavy suitcases up and down the tube (which btw, is lacking escalators in some stations).
For Children of 7 & 8, go to Hyde Park and feed the squirrels and swans there. They'll love it.
Other areas of interests maybe Legoland in Windsor , the museums (Army and British which are both free). Actually I don't recommend the tour bus since it is expensive (but a nice experience) and you can do the same trips by yourself simply by purchasing Oyster cards for the duration of your visit which provides reduced travel on all forms of transport.
Castles will be a strong attraction and Windsor castle / Tower of London will be exceptionally great for the kids.
Of course as a lifetime experience take the kids to Greenwich, the only place in the world where you can actually straddle 2 different timezones.
For food they have these chain pubs that does exceptional quality food at relatively cheap prices (6.99 pounds) for a full Sunday Roast for adults.
There's so much to do and see in London...