Also seconding a recommendation for the postal museum, the small train ride is super interesting. The Horniman museum is somewhere our kids really enjoyed, 15 mins out from London bridge on the windrush line. Also the interactive Minecraft experience on currently, friends have recommended.

In London if you go to the science museum they have a couple of payable exhibits that are worth your time: wonder lab on the has lots of interactive exhibits and shows, great for the kids. There is also a gaming exhibit. You will need to book ahead as can be busy.