Take layers. London in November will be around 30-40 degrees (maybe 50s, if you're lucky), and probably wet.
Go see:
Tower of London - you could spend a whole day here if you wanted. Very cool.
Westminster Abbey - get a tour with one of the vergers so you can see the "behind the scenes" stuff.
The Tate's - if you're into art.
Oxford/Picadilly circus - hint, if you want show tickets, you can get them at booths there on the street for half price usually just before show time. Also..great shopping here!
In ay neighborhood - wander into a pub and enjoy the lifestyle!
IMO, Buckingham Palace is crowded and overrated, but St. James Park just in front of it is lovely for a walk and nice scenery. You can walk there from Picadilly Circus, so just take a day and stroll.
The Imperial War Museum and Churchil''s Bunker (this is walkable from Westminster Abbey, and you can grab lunch at the original Red Lion pub on the way) are also cool if you like WW I and II history. DH loved those.
Notting Hill and the Kensington High Street are also nice for walking around and experiencing "life".
And finally, if you enjoy soccer...go see a Premiere League match. We're Chelsea fans, but you could do Arsenal, Tottenham, Manchester or one of the minors. The Brits don't mess around with soccer, and it's true crazy fandom! We went to a Chelsea match during one of our visits, and there was nothing like it!
Enjoy! London is one of my favorite cities!!
You can take the tube everywhere you need to go.