I'm a Londoner with five year old twins so I may not be great at making recommendations but will give it a shot!
Greenwich including the Planetarium might be good. Planetarium, Observatory and Cutty Sark all cost but Maritime Museum is free.
Imperial War Museum also probably worth a go.
Cabinet War Rooms should appeal to older kids.
The Orbit at Olympic Park has a temporary slide down in - longest slide in the world or something like that! Could combine with trip around Westfield or a swim in the Olympic pool.
If you do the Emirates cable car there is a water sports centre at the Royal docks (northern side) where you can do taster paddle board and wake board sessions - need to book in advance.
Tall buildings/views? So London Eye, Shard, Sky Garden, the Monument or go up the dome at St Paul's.
There are loads of different ghost walks not just Jack the Ripper ones (which may be a bit too gruesome!)
The Globe if they are doing Shakespeare at school.
Rib boat/speedboat trip on the Thames.