My last trip was my best ever. I took a couple tylenol PMs around the dinner service, even though I rarely use those outside of travel. I also used the eye cover Delta gave me and the ear plugs and I brought a good travel pillow with me instead of relying on the airline one. This helped me sleep through a significant portion of the flight, even though my body didn't normally sleep during that time. Avoiding any caffeine and even carbonation also helps.
Then when I get to the UK, I do my darndest to avoid naps, although I often doze off for a bit on the coach to Cardiff. It is hard the first day, but because of being a bit drugged on the airplane, I woke up in the morning as the flight was landing, and tried to go through the day normally.
Another safe and natural thing for when you get here is to bring some melatonin with you from the States (can't buy it here). It isn't a sleep pill, but helps regulate sleep cycles. I had to work with a sleep specialist years ago and they mentioned that it works with circadian rhythms (the thing that gets messed up with jet lag.) If you take it around 8 before you go to bed in the UK, it will help you get a more natural night's sleep without waking up so much in the night as I often do with jet lag. My last couple trips over have been so much better than before when I forced myself to sleep on the plane. I'm a horrible airplane sleeper, which is why the meds helped.
good luck!