I had to change GPs after 26 years, but was stuck with the nearest which I had spent quarter of a century avoiding. I, too, had to see a nurse first and there was a delay.
The nurse was lovely and very efficient and kind. There was a lot of checking of medical history etc and weighing and measuring and blood pressure and urine tests. It was all stuff that would have wasted a doctor's time - indeed, probably wasted the nurse's time - but meant they knew what condition I was in when they took me on, which was just as well as my medical records went via Timbuctoo to travel the 20 miles. I'm not sure what would have happened if they had refused to have me (I'm told that hardly ever happens) as there was/is no other option in this rural area. However, the good thing is that the nurse cottoned on that I was anxious about the switch and signed me up with a doctor indistinguishable from my lovely former GP, though I accept that in an emergency I might have to see somebody else.
I think the whole sign-up procedure is a bit of a triage, whether you come from abroad or next door, but if your prescription needs renewing you should get back to them now and if the receptionist can't help, try speaking to your local pharmacist who might be able to lean on them.