Last week we went to the London transport museum in Covent Garden. Unlike most museums here you do have to pay admission to get in, but it is valid for a year and children are free.
It is an absolutely wonderful museum. It is not huge, so the children can walk around. It is designed perfectly to push a pushchair around without bumping into people/things. There also have interactive play areas for young children to enjoy. You can go in and out of buses, pretend to drive them, walk onto old trains, even pretend you are driving a train, or fix it.
I would say if you have a young child it is a must. A real fun day out.