I totally believe you. My grandson was 4 in London last May and loved the museums. He specifically wanted to see the mummies at the British Museum and the Apollo 10 space capsule at the Science museum. He loved the Transport Museum, which is pretty much designed for kids. At the Victoria and Albert he loved Asian art. Live butterflies at the Natural History museum (curiously, he did not want to go inside and see dinosaurs).
There are opportunities for water play at the Victoria and Albert ( a courtyard wading pool) and on the southbank neat the London City Hall--- a playful fountain and little stream to float things down. Or take them to family swim time at the Olympic Park pool---it is beautiful and very inexpensive.
The kids were fascinated watching the buskers here and there, loved riding the double-decker buses, and were intrigued by the activity at the skateboard park (also on the south bank pedestrian path). Kew I mentioned above.
There was much more we could have done with them, but a week was not long enough. We had a nice apartment and enough "down time" that it was relaxing, not hectic, to get outside each dY for a park or museum excursion.
London is a great place for children.