AXA PPP Cyprus offer exactly the same medical cover as PPP do in the UK for a lot less money (its the same explanatory book), however you have to check the policy very carefully both in Cyprus and the UK to ensure that diagnostic medicine, out-patient treatment and out-patient prescription medicine costs are covered by the policy as these can be very expensive.
If you remain domiciled in the UK and are not known to be out of the country for three months or more and continue to pay UK tax and reduced NI contributions there is no reason for you to be refused a EHIC (European Health Insurance Card) by the UK authorities. To obtain these you will need to retain a permanent UK address and be registered with a UK NHS Doctors surgery. If you are leaving the UK for Tax reasons in addition to enjoying the benefits of living in the RoC then you should carefully weigh up the costs of private medical insurance X 2 etc, against any UK Tax/NI cost savings.
Reaching retirement age will not entitle you to a UK EHIC card as it is your final three years NI contributions that count and if you do not pay them and leave the UK before retirement age you will not get the cards. Currently this is being challenged in the courts.
Any private medical insurance cover costs will increase with your age, as a rough estimate consider that your costs will increase by 50% by the time you reach sixty four in ten years time and that's excluding any possible inflation. Remember you and your partner will not be covered for any pre-existing conditions. For example anyone suffering from high blood pressure will be excluded from ALL heart/circulation treatments by the policy.
If you are cutting all your ties with the UK and are going onto the Cyprus taxation system then you should apply for Permanent Resident status, certain criteria must be met to obtain this which will include proof of income, once obtained permanent residence will give you certain rights over and above the normal registration of EU citizens, as to if you can join the RoC Social Insurance scheme (for medical cover) when not working is something that you should investigate very carefully as I believe that this is not possible (maybe I am wrong). My experience of the RoC Health Service has been good to excellent, understanding the system and how it works is the hardest part but you can get help and advice at any of the Citizens Centres in the main towns, worth investigating.
Finally, although most private clinics/hospitals in the ROC operate to a high standard they do on occasion transfer patients to the state system for specialist/intensive care treatments in much the same way as private medicine does in the UK. This happened to my wealthy Cypriot sister in law who went from a state of well ordered luxury in a private clinic to a busy no frills RoC Government hospital, quite a shock for her but at least they got her well enough to complain loudly about the lack of service and having to share a side ward with three other patients
Good Luck
Nearly forgot, try down loading RoC Government forms MEU1A and MEU3A to find all the criteria that must be met for EU Citizen Registration and Permanent Residence, last pages of each refer to medical cover.