I just returned from a trip to London with my 7 year old daughter. We had an amazing time.
Quick recommendation:
Natural History Museum (tube: Kensington South)
Princess Diana Memorial Playground (north west corner of Kensington Park)
Front seat, upper deck of double decker bus (many go through Trafalgar Square, and kids ride free)
Walk along the South Bank of the Thames looking at Big Ben and the London Eye
I would actually skip the Tower (very big line ups, very expensive and very scary ... so many stories about executions, dungeons, etc.). The Princess Diana Memorial Playground is very very good. It is located at the north west corner of Kensington Park and has a wonderful concession stand and very clean toilets right beside it. You can buy yourself a drink and relax while she plays. The big pirate ship was the highlight.
I also strongly recommend taking her to the Natural History museum. It is free (most of the big museums are free and amazing including the National Gallery, British Museum ...see the world in one place, the Science Museum) and is really really interesting. We actually went twice. My daughter also loved riding on the upper deck of the double decker buses. The number 11 or the number 15 are two of the best buses. Most of the buses go through Trafalgar Square which is where the St Martin-in-the-Fields and the National Gallery are located. Be prepared to walk. London is one of the best cities in the world for walking. London is huge but central London is actually not that big. It is also one of the cleanest and safest.
Just one complaint: food in restaurants is very very expensive. (typical lunch: $40.00). We stayed at a B&B so had a good full English breakfast and ate most of our other meals from delis and supermarkets. There are sandwiches for sale everywhere, very fresh, very tasty and only a few dollars. Try Tesco or Sainsbury for good takeout.
Also, don't bother with a bus tour (headphone trouble).