Your EHIC will not cover you for a stay of 6 months..... anything over 90 days you need to apply for a yellow slip:
https://www.gov.uk/guidance/living-in-cyprusQuote:
Healthcare
If you are not paying into the Cypriot social security system you may be able to get state healthcare if:
If you are in receipt of a UK old age state pension, request an S1 form (previously E121) from the Overseas Healthcare Team on +44 191 218 1999. If you are in receipt of an exportable DWP benefit you can request an S1 form the office which pays your exportable benefit. It is your responsibility to keep the Overseas Healthcare Team or office which pays your exportable DWP benefit up to date with any changes in circumstances which may affect your entitlement to an S1 (E121). When received, register the S1 form with your local state hospital or health facility, before you register with your local state hospital doctor and obtain a medical card.
you are an early retiree and have been resident for less than 2 years, apply for a S1 Form from the Overseas Health Care Team, telephone: 0191 218 1999
you are a posted worker for a UK company ,apply for a S1 Form from the Centre for Non Residents, HMRC, telephone: 0044 191 203 7010
you are a dependant of someone who falls into one of these categories
you spend less than 6 months of the year in Cyprus and have a valid UK European Health Insurance Card (EHIC)
If you do not fall into one of the above categories and are not paying into the Cypriot Social Security System then you will not be entitled to free treatment and should look to take out private health insurance