I don't know how sensitive you are, but you might find a long day at the Imperial War museum somewhat draining emotionally (well, I did anyway!), so it may be better to split up visits.

When at the Science Museum, the Natural History Museum and the Victoria and Albert Museum are adjacent. The V&A is a nicer place for refreshments anyway! It's definitely worth checking the plans online, there may be something there that interests you.

For more science-related stuff, the Royal Institution is worth visiting, although it won't take very long it isn't far from Green Park. UCL also have a couple of museums near the British Museum. I would only suggest the Petrie museum if you have a genuine interest - lots and lots of pots in glass cases isn't for everyone!

Personally, I found the Museum of London a little tedious - but rather enjoyed the Museum of London Docklands. And if you are out that way, there is also the maritime museum in Greenwich.

Don't forget to allow some time to relax!