Five years ago, thanks to British Air not having enough crew to fly an airplane back to Seattle, we were gifted a layover day. Took the tube in from Heathrow, walked from Picadilly Circus to Trafalgar Square to the House of Parliament to Buckingham Palace and then back to the airport. In just a few hours walking we saw a lot, including many monuments to The Empire (the lions at Lord Nelson's feet are slightly oversize), as well as the stunningly understated memorial to the Women of WW2. Certainly didn't see everything, but appreciated all that we did see.
So, along with any tour, just get out on foot and look around.