In my option the hardest airports to fly into or out of in the United Kingdom, is London Heathrow and London Gatwick. The volumes of people going through customs and the amount of arrival planes is tremendos. Sometimes it can take up to 3 hours to pass through their customs. Planes leaving the United States for London Heathrow or London Gatwick are mostly in the evening which arrives the following morning when you are the most tired from travel. You will walk forever at either airport from your gate to customs only to wait in large lines.
May I suggest you fly into Ireland, Scotland, or Wales from the United States. Spend a couple of days seeing that country and catching up on your sleep. This last trip we flew into Edinbaugh and walked straight into International Customs with no wait, then caught a taxi which took us to our Edinbaugh hotel. Our rooms were marked as Early Check-in. We had an early lunch and drinks relaxing and then going to bed early. We were up at 6:00 AM the next day ready for our Scottish tours and travels. No jet lag for us!
We left Edinbaugh, Scotland on a domestic flight to Southampton, United Kingdom for our cruise and walked off the airplane and straight into a taxi. International Customs had already done in Edinbaugh.
Once you have entered the United Kingdom you are good to travel in and out of those countries. Take a domestic plane, rent a car, take a ferry, or a train to get you from place to place.