As others have noted, you have a chock full itinerary, even without the British Museum. I'm not trying to add to it, I just wanted to suggest something you may not have considered, perhaps in lieu of something else (maybe Buckingham Palace), and that's a guided tour of the Palace of Westminster (aka the Houses of Parliament).
We did this in 2018; the tour is about 90 minutes long, and it was one of the best tours we've ever taken, anywhere. The Palace has incredibly opulent rooms, and you walk through many of them, learning about history and about what you are seeing. And then, a major highlight, we visited the Chamber of the House of Commons. We got to stand in the rows of seats (only elected Members may sit in those seats, as we learned) while the guide discusses what happens in the Chamber, who sits where, the history of the Chamber, etc. It was a "pinch me" moment to actually be inside such an iconic place that I'd only seen on TV. (And I say that as an American.)
Just throwing that out there (especially since your hotel is so convenient to Parliament).
https://www.parliament.uk/visiting/visiting-and-tours/