(2-part post):
I used to organise school trips (from Sheffield) to London, for 11 & 12 year olds and I've taken dozens of other youngsters there at various times, so I think I know what your family might enjoy. Here are my thoughts:
1. Give the open-topped tours a miss. Children find that the novelty of sitting on the open top deck soon wears off and they quickly get bored. (The tours are also very expensive).
2. The Science Museum is an absolute 'must'. I've had difficulty persuading some children to visit it but I've always had to drag them out of it, three hours, or even five hours , later ;-)
3. Most of the Science Museum is free but it's worth paying for the Imax cinema and the special exhibits:
http://www.sciencemuseum.org.uk/visitmuseum.as px
4. The Natural History Museum is just round the corner from the Science Museum. You might not want to visit all of it but I strongly recommend visiting the moving dinosaurs (at the far end of the dinosaur gallery):
http://www.nhm.ac.uk/visit-us/galleries/blue-z one/dinosaurs/index.html
5. To do a bit of sight-seeing (but without boring your children by taking too long over it), take a river trip from Tower Pier to Westminster Pier. It takes around 30 minutes and you see lots of the major landmarks. (As far as I'm aware, you still get one third off your fares if you show a Travelcard). The boats leave roughly every 20 minutes. Timetables are here:
http://www.tfl.gov.uk/gettingaround/1131.aspx# ************
6. There's usually some good, free street entertainment at Covent Garden