Hi I have kids similiar ages and we went to London over this weekend, infact we go regularly..
The Natural History museum is a MUST for us as they have animated dinosaurs there, plus it's free! Just visited the newly opened Aquarium, very impressive, thats on the South Bank. It would be about 50 quid but we had some Tesco vouchers, so look out for those. We don't do Tussauds as my children arn't really into celebrities and it wouldn't hold their interest. My youngest is also very sensitive so we can't do the Dungens or the Tower. We have also been to the Science museum where there is something called Launch Pad which is a hands on investigation station, also some free shows in there, well worth a visit and with Natural History and Science very close you can do both in a day and both FREE. As someone already said take comfy shoes, clothes and plenty of water, as London is very draining! BUT FUN!