Try these tours:
http://www.newlondon-tours.com/daily-tours.html
I would suggest the free tour of London, where you'll see this:
Hyde Park Corner
Buckingham Palace
The Changing of the Guard (most days)
Churchill’s War Cabinet Bunker
The Houses of Parliament
St. Martin-in-the-Fields
Westminster Abbey
Trafalgar Square
Nelson’s Column
Wellington Arch
St. James’s Park
10 Downing St.
Horseguards
Big Ben
If you have energy left, I also suggest to do their pub crawl.