mikey; You do not have an automatic right to free healthcare in all EU countries, if you are travelling you need to have a certificate from the UK; but this usually only applies to emergency treatment.
http://www.nhs.uk/NHSEngland/Healthcareabroad/plannedtreatment/Pages/Introduction.aspx
In other EU countries the system is that everyone must have health insurance in a similar manner to having car insurance i.e. through an insurance company. If you are Senior Citizen and wish to
reside in another (but not all) EU country you have to, like everyone else, register with a private company and you are given a plastic card (with photo), which because of your age is free, people below retirement age have to contribute. This is swiped whenever you visit your doctor or receive treatment. The fee for this is initially paid to the doctor by the insurance company who in turn claim it back from the NHS.
So if you are beyond retirement age and want to get a first class treatment paid for by the NHS you can do no better than move abroad. I won't list here the other benefits :0)