I'm pleased to see the Science Museum at the top of your list, as it's the most obvious place to go with kids. The Natural History Museum is right next door and, even if they miss out the rest of the exhibits, it would seem silly to miss out on the dinosaurs. (The moving one is great for kids!). Both the Science Museum and the Natural History Museum are free (unless you pay to visit special exhibitions within them).
More museums for kids here:
http://www.timeout.com/london/attractions/top-10-museums-in-london-for-kids
Other than that, a
brief boat trip is well worth considering. (Kids get bored on long boat rides and it can be ruddy cold on the Thames in January as well!). The ride from Tower Pier to Embankment Pier only takes 17 minutes but it takes in loads of sights (including Tower Pier, the Tower of London, HMS Belfast, the London Monument, Cleopatra's Needle, etc). That positions you well for a look at the London Eye (with perhaps a ride on it if the queues aren't too long) and the Houses of Parliament. (River buses run every 20 minutes on that route).
Having mentioned HMS Belfast above, I'm reminded that every child I've ever taken there has really enjoyed the visit:
http://www.iwm.org.uk/visits/hms-belfast
If the weather's good, the street entertainers in Covent Garden are always worth watching.
More ideas here:
http://www.timeout.com/london/kids