If you have a layover, as I did, London tour companies offer hop-on, hop-off tours for 16 pounds. I chose the Big Bus Company tour. The guides are knowledgeable and try to entertain as well. LHR offer luggage storage for about 5 pounds per bag, good to know if you’re planning on leaving the airport. Most tours and hotels revolve around the Piccadilly Line, which the Express Train does not go to without a transfer. The Tube is slower but cheaper and direct.
Big Bus tours are located 2 blocks over on Coventry, once you come above ground (from taking the Tube exit the Piccadilly Circus stop). A return adult Piccadilly Line ticket on the Tube is 7.60 pounds. Be prepared for the crowds on the Tube. It is a major source of commuting for many Londoners.