It all depends on whether the Doctor has qualified. Is the doctor qualified inside or outside the EU?
If the doctor is within the EU and have been working in the EU, then the assumption is that they would be able to diagnose and write prescriptions in the UK without undergoing further examinations.
If the doctor is outside the EU, they would first need to complete and pass the PLAB Test before being qualified to provide medical advice in the UK.
A doctor outside of the UK, cannot issue prescriptions for people in the UK. These can only be done by a private medical practitioner who is licensed to practice in the UK or an NHS employed doctor.
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If you wish to discuss, please feel free to ask further questions.
Any EU Doctor would have to register with the GMC but would not be required to sit the PLAB test.
You are correct in assuming that the general requirement is registration with the GMC.