Hello Kevin. If you will arrive at an airport of London at 1 P.M. after being in an airplane all night, I do not recommend trying to do any sightseeing that day. Your airplane could arrive late at the airport, and getting out of the airport (Heathrow or Gatwick) can take 1 and 1/2 hours, or 2 hours. When I arrive there, I want to immediately go to a hotel, have a shower, and sleep for 2 hours. Recently a person, at this Traveler's helpline, said she was awake in the airplane all night, and when she arrived in Europe she was physically active all day, to get adjusted to the time zone there. That caused her to experience a brain seizure there. For your second day in London, I think going to only the British Museum is enough. When you leave it, perhaps you could ride in a taxi to Covent Garden for people watching. If your flight from London will be from the Gatwick airport, a good way to go to that airport is to ride in the "GATWICK EXPRESS" train from Victoria Station. Tickets for the Gatwick Express train can be purchased the previous day at Victoria Station. Your baggage can be parked at Victoria Station. ("Left Luggage"). Read about hotels located in back of Victoria Station (south Belgravia), in any of Rick Steves' books : LONDON, or ENGLAND, or GREAT BRITAIN. I recommend : plan to arrive at the airport at a time that is 2 and 1/2 hours earlier than your scheduled departure time.