It depends on where you're going to live and whether you want to go public or private. The best public (called state schools in London) schools may be fully subscribed as well.
A couple of neighbourhoods to consider: Clapham in the south will have lots of families and good selection of private schools, Wimbledon/Putney are also a good choices in the Southwest, St John's Wood in NW is home to the American School in London and has lots of expats so will have many choices. There are some good schools in the Crouch End/Highgate/Muswell Hill areas of North London to choose from as well.
Others from London will be able to provide you with even more ideas. almost 7 years ago