You should be fine, especially as you are in Biz Class over the water.
Take 10 mg Ambien on the eastbound (US-UK) leg and sleep well.
Take 3 mg of Melatonin (purchase in US, over the counter) at bedtime for the days you are back in the UK.
Whatever you do when you arrive back in the UK, don't fall asleep for a long nap. Stay awake the first day until at least 9 pm. 10-11 pm better. Then sleep through the night.