They were very obliging when they thought I was an offcomer, but then refused once they saw my address, and that I was already registered with another practice in town. When I checked with the Health Authority told me that they have a form for applying to change surgeries, but you can't choose which one, and have to accept whichever one they allocate you on a take it or leave it basis. The NHS website says whether surgeries are accepting new patients or not, so that presumably means practices have the freedom to decide not to accept new registrations if they consider they're 'full'. Given the endless complaints from GPs about being overworked, I can't see any of them exactly being ecstatic about taking on more work.
If people were completely free to pick whichever practice they choose, you could reasonably expect that almost the whole town would want to be with whichever one has the best rating, whilst the others are left with almost no punters at all. That's not a workable system, particularly for any resource that's both free at the point of use, and in short supply, which is doubtless why the HA told me you have to take what you're given. It would be no different to the whole audience insisting that they sit in the seat with the best view in the theatre.