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What I thought were Allen bolt adjuster screws just seem to hold a bolt cover on.
It appears to stop the door rubbing that you lift the door off and move it one serration along on the hinges.
The door won't lift off and I can't unscrew the door from the hinges as there seems to be bolts coming from inside the actual door.
Are my assumptions correct? Do we need more oomph to get the door off?

The black bit in the centre doesn't have an Allen bolt. There doesn't seem to be any threaded adjustment at all.
I can’t unscrew the door from the hinges as there seems to be bolts coming from inside the actual door.
seems to be? Have you tried undoing the screws? They could be locating pins to register the hinge in place and support its weight the screws would then just be preventing the door slipping of those pins rather than holding the weight.
If you do a image search for UPVC hinges you'll see many of them have little studs as part of the flag
I'd have thought that part of the hinge would release from the door when those screws are undone but the weight of the door is hanging on those two pins so it might not be apparent that hinge is free to move when you unscrew it.
Then you'd be able tap that flag of the hinge up off the spigot with a hammer and adjust them one at a time without having to deal with the weight of the whole door