I don't understand why you say this.Good morning,
There is NO national health service in Cyprus.
The state hospitals and GP service are the frontline of the national health service here. As I understand it, it is a contribution based service just like the UK but eligibility ceases when family earnings are over €30,000.
If you have eligibility form the UK this is the national health service you can use.
If you feel I am wrong could you please explain the existence of the state run hospitals.