You're all adults. You probably don't have identical interests. You may find there's quite a difference in how much time is desired at some stops.
Perhaps the best example of that is the Churchill War Rooms. Some folks just want a quick visit to the basement rooms where critical wartime decisions were made. There's an audioguide that doesn't take a great deal of time, and conditions are quite crowded, so that aspect of the site won't consume too much time. (It's my contention that the place is seriously overpriced if you only want to see the war rooms.) The real time sink is the (excellent) Churchill Museum section. There's material to read, there are film clips to watch. This is where some people can spend a great deal of time. I spent well over half a day at the CWR, maybe close to 6 hours.
So my suggestion is to try to allow some flexibility in your scheduling for individual members of your group. I have no specific suggestion as to how to do that. I just know that I hate leaving a place I'm really interested in when 5there's more to see--all the more when I've paid a $30 entry fee, or whatever the CWR cost these days.
The V&A is one of the museums open late one night a week. However, I think only the ground floor remains open (ask at Information desk; I don't believe you can find out from the website). Also be aware that the part of that floor under the skylights can be a bit dark when the sun goes down. The best area to see late in the day is the area not under the skylights.
If you are interested in the V&A's fab jewelry collection, get to the museum when it opens and head there first. That's the only part of the museum that has ever been so crowded that it affected my ability to move through the exhibit and see the displays. In my experience that section remains uncrowded for at least 30 minutes after the museum opens, which makes for a much more pleasant and efficient visit.
The V&A has a wonderful wrought iron section that might appeal to someone not interested in jewelry, ceramics or glass.
The British Miseum is very heavily visited. I was told the Egyptian section is the most mobbed and that rainy days are the worst. I believe it, too, has a late-night opening, as does the Tate Modern. Unfortunately, there's a lot of overlap in the museums' late-opening schedules. I think Friday night is a popular time for museums to be open late.
Edited to add: Pre-COVID, the Tate had music on its late-openg night and attracted a large, lively, young crowd. That could be fun or a bit annoying, depending on what sort of music you like. I guess it might also be a bit uncomfortable if anyone in your group is especially concerned about COVID.