National Army Museum - has a fab themed soft play (best to book a time slot ahead online in advance) and much of the rest of the museum is very child friendly. I've been a lot with my two and the War Horse exhibit in particular is great, plus the dress up stuff in the Boer War bit. Museum is free. Small charge (£2.50 I think) for the soft play. Natural History is awesome. Tate Modern has a very very small kids play area.National Gallery does a kids activity thing on a Sunday morning.
Of all these the army museum gets my vote though (after the science museum!).
In the basement of the Natural History Museum is Investigate, the poorly advertised hands-on bit. It has microscopes and computer stuff, homonid skulls and loads of bugs in perspex. It's mainly aimed at older kids but my 3 year old loved it too.