It's not only doctors Jan it's scientific research in general which is international. It was ever thus.
There is no reason any of this should change post-Brexit.
I have a close family member who is a leading researcher in photo-voltaics at Imperial. His team here is truly international and his research takes him to South Korea & USA as well as Finland and other EU countries.
The idea that post 2019 he will continue co-operating with the rest of the world whilst shunning anyone from the EU is ludicrous to the extreme.
The world has always been slightly larger than the EU. Is it any wonder that one in ten countries are led by someone who has been educated in Britain?
Personally I'd like to see a new scholarship scheme designed to ensure that hundreds of the EU’s brightest young people are brought to study at UK universities every year, to show we’re not pulling up the drawbridge.
People with skills and talent will always be able to settle almost anywhere they want. They always have. Which is why I'm still in the UK!
(thought I'd get that in before someone else did) 