All official statistics disprove so-called health tourism. Immigrants are significantly less likely to use the NHS than those who are born in the UK (because they're overwhelmingly of working age, so they are a lot healthier than our ageing population). The main reason for migration to the UK from less developed countries is to find work and most immigrants have work before they even come here (ironically it's often in the NHS).
It would also be against a doctor's hippocratic oath - quite rightly - to refuse treatment to someone who needed it, so I hope that this levy would not mean that immigrants new to the country are refused treatment.
I also hope non-payment of the levy due to serious mental health problems, drug abuse, homelessness or poverty would not count against someone who needed treatment.