Realistically, the only place for doctors to move to is Australia, NZ, the US and Canada, as most of them probably don’t speak another language well enough to move to a non-English-speaking country (and to do all the training needed to be a qualified doctor in that country).
Australia and NZ are both very far away from the U.K. and with huge time differences, so that is a major move. The US and Canada are closer, with a smaller time difference, but it’s still a big move. People won’t uproot themselves - and their families, if they have a families - for that sort of move unless they’re desperate.
Anyone wanting to move to these countries will also need to get a work permit and a job there, and also find somewhere to live, before actually moving there. It takes months to do all of that - at least a year.
So if they’re moving there between now and say Christmas, they would have had to start planning the move a year ago. Given all of that, I don’t think we’re going to see a massive exodus of doctors any time soon.
In fact, I’d suggest they’d be tempted to stay because, unless they already planned to move, it’s a big hassle for them to move and their wages will also (finally) go up under Labour.