Just took 3y9m DD and 14m DS yesterday. DD was in raptures, though a bit scared of the 'robot dinosaurs'. DS just wanted to crawl around the floor and climb the stairs! Our train journey was only 40 minutes and there was standing room only, DS was a royal pain throughout!
I would recommend the explorer backpacks that they do (for free) for under 7s. Which include some clues (like fossil claws), an explorer hat, binoculars, magnifying glass, pens & paper. DD felt just like Dora the Explorer. You can choose one dependent on the exhibits you are visiting.
We managed 2 hours in there (including lunch) before our two were begging to get out. We saw the dinosaurs and the mammals bit. They have a skating rink until the 9th Jan, DD was desperate to have a go because they had little push-around penguins for the kiddies to help balance (but we didn't let her cos neither of us wanted to go).
If you want something else to do on the day, then Covent Garden is good for the street performers. We also head to the South Bank becuase there is usually lots going on - gawp at the Eye, street performers, sometimes markets, nice eateries. The cafe at the British Film Theater is good too, lots of comfy chairs and they are pretty relaxed about kids running about (the entrance is tucked away down a side bit though, you wouldn't bump into it)
Have fun!