I’m not British, so I suppose I don’t have a dog in this particular race. But as I understand it, even a hard Brexit doesn’t mean no immigration, it just means immigration is controlled by Westminster rather than Brussels. So there’s no reason the UK can’t still admit all the doctors and other desirables who apply whilst rejecting unskilled labourers and economic refugees of dubious provenance. Have I misunderstood?
(Note that I’m a fan of free movement generally and that what I’m describing is not my personal position. I’m just willing to try to understand the positions of those with whom I disagree.)