Julia,
I've only been in London once (I was up for a CWA Dagger for a novel that's still unpublished, darn it), but, fortunately was able to stay with family (my Irish immigrant grandmother had 19 brothers and sisters, one of which wound up in London, so I had cousins I could stay with).
I'm not familiar enough to make many recommendations, but your trip reminded me of a short film called "From the Four Corners" I saw a few years ago in which three Commonwealth soldiers, one from Canada, one from New Zealand, and one from your own country (God bless a place that produces a Jon Cleary
and an Arthur Upfield), when they meet the famous actor Leslie Howard. He takes them around the town, and talks about the shared heritage they all have as citizens of the Commonwealth, the heritage they're all fighting for.
Dandy film. You can find it here:
https://www.youtube.com/watch?v=z0UF36Nyg58&list=PLNsVXeTWRxyiqZRKvQS0xBHqtbhIrUtZW&index=12
Check it out.
JIM