Hi
Natural history museum is great for that age but v busy. It's ok if you can get there for opening time at 10 and to be honest by the time it gets packed they will have had enough. Under no circumstances arrive in the afternoon in the school hols ! If they like dinosaurs aim straight there at 10 and you'll be fine.
Science museum also brilliant. The launch pad section is interactive and will keep them busy for hours. If they like planes then go to the top floor flight section, much quieter! Again arrive at opening time. Both of these are close to a park for the afternoon.
Museum of london - good Romans
British museum - good for mummies and has a dehydrated body they can look at too. Mine was vv ghoulish before you ask.
London transport museum you have to pay for but lots of fun and you can clamber on all the old trains and buses. The ticket lasts a year for reentry. Plus it's in Covent Garden so you might be able to do some shopping afterwards ?
Tate modern is lovely - I took DD loads at that age. Pick one or two rooms to look at, let them run round the turbine hall and then walk along the southbank to Waterloo. Lots of activities happening especially at the weekend. If you start at London Bridge you are right next the golden hind too.
Greenwich is also good (not sure where you are coming in to). The maritime museum is free and good fun, lots of interactive stuff to do. The Cutty Sark is fab but v expensive. The park is good to run a round / roll down the hill and has a playground. And the planetarium has fairly cheap star shows.
What sort of things do they like? I can suggest more .......