Thing is, though, May wasn't speaking for 'britain' or the 'british' NHS - since there ain't no such animal. Scotland's NHS has been separate since 1947, and the various devolved governments have had no issues with the import - or indeed export - of skilled professionals.
Neither, to be fair has the UK government up till now.
In 2015, net immigration was about 330,000 people. Just over half of them were from the EU. However, the remaining half were from outside the EU which means we don't have to let them in. So, if immigration is such a huge problem, why didn't the government cut it in half?
There is no political will to deal with the immigration "problem" for a couple of reasons:
Immigrants tend to be net contributors to the government's coffers. They are more likely to be paying taxes and less likely to be using the NHS and drawing a pension than the indigenous population.
The problem isn't really a problem at all. 330,000 is less than 0.5% of the population and that is a historic high. Once Brexit kicks in and the economy tanks, we'll probably find that we have net emigration. The UK population is only going up at all because of immigrants.
Finally, 330,000 is just a number. Reducing it to, say, 100,000 is a story, but it's a pretty abstract story. "UK Immigration officers deny mother right of entry to be with her husband and children" is also a story but it's a human story that people can relate to. If we significantly reduce immigration, we'll get many more stories like that. That's the kind of publicity the government doesn't want.
