Where do you assume they are not in good health?
Or many of them are not in good health?
Most of them are university students or economic active people as far as I know.
Cutting those places will put UK in even a worse place then after Brexit.
For sure there are sick people. Over any population there is a sample which is sick, but how much is it according to you or your sources?
I don't think, nor I have proof, but seems logical, that there will be many more healthcare workers than sick people.
The real mess is not about immigrants, I cannot blame them for the lack of investiment, training and planning over 20 years or more.
If anything, I am grateful that if I go to a hospital they can admit me because there is AT LEAST enough people.
It seem lack of character to change policies after asking people to come.