Either the Natural history Museum and / or the Science Museum (they are next door to each other) The science museum has Launchpad - a brilliant hands on section. NHM has dinosaurs, the blue whlae, and other excellent sections. Go up the escalator to the earth sciences part and experience a fake earthquake, for example. Both these museums are free.
Or
Take a boat down the river to Greenwich. The Maritime museum is good (and free) or walk up the hill to the Observatory, stand on the date line, visit the free astronomy museum and maybe pay to see a planetarium show. You can easily get the overground train back to central London from Greenwich station, or go back on the boat.
Or
The Covent Garden area - The Transport Museum would be a smash hit with a 6 yo, (there is an entrance fee) , wander round and watch the street performers, have something to eat and then stroll the 5 min walk to the Lion King
Or
The South Bank - the Aquarium is excellent, rather expensive but you can use tesco vouchers etc, the London Eye, walk along and see the street performers. You can book a timed slot for the Eye - or queue, the queue goes faster than you think.
(The boat takes hours to get to Hampton Court - much better visited by overground train from Waterloo, IMO).