When I was a dental student in my fourth year we acquired a new Professor of Prosthetic Dentistry, imported all the way from Melbourne, Australia.
It was the era of Monty Python's Flying Circus and the entire student body immediately referred to him as 'Bruce', both in and out of his hearing, talked about our pins and pincils, and of course the dintures we were busy making for our patients.
Sadly we couldn't understand a word of his lectures, but whether that was due to the accent or the content is debatable
Returning to the OP, EU qualified doctors at the moment don't have to take any test to prove their proficiency in English