I've been in similar situations on my TT trips. On a few of those, we rented our bike in London. We'd show up and take a few days in London before heading out. It has so many attractions, you'll just have to pick a few and try not to do too much. Consider it a recon session for future trips. We focused on museums, and even then, barely scratched the surface. Spent a day at the British Museum, but didn't have time for the Victoria and Albert. Did some touristy stuff (Sherlock Holmes) and some biking stuff (Ace Cafe). Just remember, like NYC, London isn't "like" a lot of the rest of the UK in many ways. Learned this from bike touring the smaller areas. Costs, people, customs, services, etc. are a lot different. Even in those smaller areas, we never lacked for interesting things to see/do. For somebody from the states, everything was a wonder, even after multiple trips.
Too many things to list but I will throw out a couple I haven't seen mentioned yet: The Imperial War Museum / Churchill War Rooms should be on any short list along with the British Museum. See a show if any look interesting to you. The quality of the acting beats Broadway, IMHO. The music scene can be good too. We caught an organ concert at St. Paul's Cathedral, and it was amazing. If you want out of London for a day, you can take a day trip by train to Cambridge and go punting on the Thames, etc.
This was fun too. Touristy but cool to put the stories in perspective by seeing the actual locations where it went down. https://www.jack-the-ripper-tour.com/
Be prepared to spend a lot of money, things aren't cheap there. If you've only got a few days I would suggest staying in London, there is a awful lot to see and do, however some things might already be on "winter hours" so they might not be open as long. A couple of the tours suggested might be fun and if you like museums there are some very good ones there but I would be prepared to spend a day in the one you choose to visit. The usual sights come to mind, the Tower, St. Pauls, Houses of Parliament, Buck House etc., might be worth taking one of the bus tours to see those. I'd suggest using the underground, you should be able to get a travel card which gives unlimited travel for a day within the zone it's for. Don't know how you managed to snaffle a ticket for the footie but you're lucky. The Gtech Community Stadium isn't very big but the game against Chelsea is a local derby so the atmosphere will be really good. Shame it isn't at their old ground, Griffin Park which had a pub in each corner.