eSim is the way to go. As previous posts have mentioned, a lot of the new phones (especially iPhones) don't allow you to access the physical SIM card, so eSim is the only choice. And even if you are able to change the SIM card physically, why do you want to (1) waste an hour of your precious time at Heathrow, and (2) do the swap in a busy airport with this tiny plastic piece that you will have to replace and then save the original SIM in a secure place for the whole trip?
I have traveled to Europe many times over the last decade both for fun and for business, and I always use Airalo to buy an eSim ahead of time. It's very economical and you can install the eSim while in US, then switch to the new eSim upon landing at the airport. (They provide very detailed instructions, both in writing and in video, on how to do this.) If you are only there for a week, you can get a 1GB data package (with 7 days validity, starting when you first use it) for $7, and you can get a 2 GB package (with 15 days validity) for $10.50. On our last trip to Europe for 9 days on the ground, we used 1.3 GB, primarily for Google Map navigation when we were out, while relying on free WiFi at the hotel/Airbnb and many public spaces (museums, restaurants, and etc.)
The only downside of eSim is that you cannot do voice calls. It's data only. My experience is that nobody uses voice calls nowadays. Everybody uses texts or emails. If you really want to call a local restaurant or shop, you can use WhatsApp, which uses data.
We also found a discount code that gave us $3 off any Airalo package, so you can pay as little as $4 to cover your data needs in UK. The code is MINFEI4587.
Good luck and enjoy your trip.