It is my opinion that U.K. citizens who are already living/working in Cyprus, or any EU country, will keep that right should the U.K. decide to exit the European Union.

I say this because the Vienna Convention of 1969 states that the termination of a treaty “does not affect any right, obligation or legal situation of the parties created through the execution of the treaty prior to its termination.” The House of Commons Library says that “withdrawing from a treaty releases the parties from any future obligations to each other, but does not affect any rights or obligations acquired under it before withdrawal.”

I must clarify here though that the above is only applicable to those U.K. citizens who became expats in Cyprus (or another EU state) before Brexit.

As far as health services go I believe it is unlikely that U.K. citizens would be denied  EU health care services as the U.K. could retaliate by refusing these services to EU citizens living in the United Kingdom.