Oh, sounds like an exciting trip ahead of you! On the topic of London recommendations — off the top of my head, some less-known ones would be the London Wetland Centre in Barnes, if you like looking at birds (take the tube to Hammersmith and then walk across the poor crumbling Hammersmith Bridge, or else bus, plus if you go into Barnes Common there is a tree there that is one of the oldest in London); the Hogarth House in Chiswick (not far away from Hammersmith either), which is delightful if you like William Hogarth or are interested the 18th century; and the National Army Museum, which is one that not a lot of people have been to, but I found rather good when I went a few years back.

I've asked my partner (a Londoner), so hopefully there will be some additional recommendations :-)