You can switch your Apple ID's region to another country, enable ADP then revert your account's region back to the United Kingdom. You've got to leave Family Sharing first and may also need to adjust/cancel subscriptions - I don't think it's totally straightforward.

I've not looked into it but I suspect this uses eligibilityd, the same thing that does the location based checks to see if EU users can use 3rd party app stores.

From what I remember it uses a combination of things like your current GPS location, your SIM cards reported country and more to determine what country you're really in to restrict certain features.

So it's not as simple as swapping your location in settings, or even traveling to somewhere in the EU, theres a certain sticky-ness to what your device thinks is your current country.

Edit: bit more info on eligibilityd here https://theapplewiki.com/wiki/Eligibility#eligibilityd

Yeah, good point. I wonder what would happen if someone without ADP in the UK changed over the region settings to the United States, switched ADP on, and then switched the region back to the UK. I wonder if anybody's tried this?

I think country is associated with the iCloud/Apple ID account, not the physical device.