I think a full museum visit can be too much for young children, myself included, I'm often interested in only one or two sections in the large free museums.
Children can be fascinated by normal things, like riding the underground and using the long escalators and ticket gates.
I agree with suggestion of riding top deck of a bus, use the proper public buses not a hoho, your children will ride free with you.
Agree about a river ride, take the faster Thames Clipper river bus, not a tour boat.
Take them for a ride on the front seat of a driverless DLR docklands train, a rear seat view is good too. There is a foot tunnel under the Thames between Island Gardens and Greenwich near the Cutty Sark.
The London Transport Museum Covent Garden has stuff for youngsters.
A walk in St James's Park, this has lots of wildfowl, lakes and small bridges, a cafe too.
London Eye too, What's different is you ride in a large glass capsule, you are free to move around.