The Foreign & Commonwealth Office offer specific advice on each country on their website. Look very carefully.
Often there are reciprocal arrangements for emergency care, but exact definitions can vary. In some countries services are offered in such different ways that it can be difficult to compare. The definitions of institutions such as 'clinic', 'nursing home' etc. may differ.
Also be aware that your entitlement to some services in the UK may lapse after a period abroad.
I think that if you asked about a specific country, some nans might be able to advise, or direct you to websites that might be useful.
Regarding prescriptions: arrangements are being made with individual countries. But what you can buy 'over the counter' also varies, so that may be helpful.