Two notes about The Tower of London-- tour with a beefeater (free, they post the times of the tours, and these guys are funny). Second, see if you can get a pass for The Ceremony of the Keys. On one hand, it's much easier to book now than when I did it because you can book online, but on the other hand it fills up much faster because it's easy to book online.
Also, when you're in the area of The Imperial War Museum, consider going to "The Grapes" (Limehouse, on Narrow Street). Things may have changed since 2012, but I had the best fries "chips" ever in that little pub. So amazing that I'll go back someday, just for those fries.
ETA: Also, if it's your thing... We did the Jack the Ripper Tour with London Walks. I made sure to book a night when Donald Rumbelow was leading the tour (and made sure to get into his group when things split). I don't know if/how often he leads walks anymore, and I'm sure the other guides are great too, but it's really cool to see him on shows like Murder Maps, or hear him in a pod cast, and remember that night and that tour (where, of course, I also spent 10 pounds more and bought his book from him, that he autographed at our last stop for the night).