Bar-B-Lew,
I have been to Europe many times, mostly on business as my company was based in the Netherlands, and my particular part of the business in Amsterdam. Mind you, I am on the west coast and the flight is much longer and the time zone difference much greater. You have received many great tips! Based on my numerous flights, this is what I would prioritize:
1. DO NOT go to sleep when you get there. You will be exhausted, but power through. If you go to sleep it will take much longer to acclimate.
2. Try to wake up 2-3 hours early the day of the flight to start to transition your schedule. For the two days before is even better. May be more difficult for you because your flight is so late. Mine were always around 2 pm.
3. Try to get an hour or two of sleep, but was never easy for me, even in Business Class with seat that make into a bed (company perk!). This is the reason for number 2.
4. Drinking alcohol to sleep is ok, but if you do, drink twice as much water as you would otherwise. Dehydration makes jet lag worse. Alcohol and the air on airplanes are not a good combination for long flights unless you drink a lot of water.
5. Bring a sleep aid like Tylenol PM, but not for the plane trip. Take it the first couple of nights to help you sleep. As tired as you will feel if you stay up your day of arrival, sleep will still NOT come easy.
6. Ear plugs and eye shades are essential. You never know who you will sit near and many watch movies the entire flight and make much more noise than you think.
7. Power Adapter is a must. Not sure why I put it as #7, but I was more focused on jet lag.
8. Have a picture of your passport on your phone, and paper copies in suitcase as well
Have a great trip! Never been to London, but Amsterdam is wonderful/intersting! I was fortunate enough to spend many weeks there.