Everyone has a different strategy, but in this mine would be: lots of sunlight, no napping until bedtime, low-stakes activities, normal rise the next day.
Lots of sunlight -- light has an influence on your body's internal clock, via melatonin. I realize London isn't always sunny, but if it cooperates you should spend time outdoors!
No napping -- your arrival is relatively late in the day so this probably won't be as much of a concern, but strive for a relatively "normal" bedtime, say 9 pm or so. If you nap for hours immediately upon arriving at the hotel you may have trouble falling asleep that night.
Low stakes -- don't do anything that is a "once in a lifetime" or expensive paid tour or anything like that. You'll be in a bit of a haze so don't do anything where you want to be 100% present for the experience. I like running "errands" on the first day (pick up SIM card, maps if going on a road trip, any needed supplies) that I've mapped out on the first day since then I can be on autopilot, knock out all those tasks, and spend time outdoors moving from place to place.
Normal wake-up time -- you might want to sleep in until very late the next day; don't. If you can manage a relatively normal wake-up time it will help you immensely.