If are of UK retirement age and you receive a UK
state pension (not an occupational one which you may get earlier). Then you may obtain a form S1 which entitles you to obtain health care in another EU country on the same basis as nationals of that country (so any costs paid normally there will have to be paid by you). In the case of state retirement pensioners, the UK will actually still be covering your care but it will be paying Italy for it.. It's more complicated if you don't have this and you may have to obtain private health insurance.
(see this link; it's a bit out of date as it calls form S1 form E121 but it seems accurate otherwise; check though yourself for any recent changes)
http://italy.angloinfo.com/healthcare/health-system/eligibility/
You will be able to get both emergency care and 'ongoing' care with an EHIC if you visit for short periods (which the UK actually also funds for state pensioners!) This doesn't include going back to the UK specifically for regular check-ups.
(some people do manage to do this by keeping homes in the 2 countries , spending 6 months in one and 6 months in the other so keeping their UK health care status.. sometimes their 6 months is stretched a bit but that's not strictly legal.
As to the dream. I have lived in France now for 13 years much of it very good. We have done lots of things that wouldn't have been so easy in the UK. I've had a lovely house and garden (lot's of work there though!) been able to swim in our own pool in summer with lovely al fresco meals, to go skiing in winter for far less money than I could if in the UK. I've been able to visit many beautiful places and met lots of new people.
There is a flip side which it is important to think about.
Make sure that you can speak reasonable Italian, health care and everything else can become very difficult in another country.
Think about how you will feel being a long way from friends and family. They will love visiting you at the start but probably not so much in later years when the novelty has worn off or their circumstances have changed.
If you have family back in the UK, think about how easily you can visit them in an emergency (do you have parents still living?). Consider the fact that exchange rates may change and that 10 years down the road, financing visits back may be more difficult.
Lastly, think about what will happen if you become older, or more infirm or if your partner does. Make sure that either of you will be able to cope on their own. Will you be able to return to family if you need care? (remember much of the care of the elderly in Europe is done by family, and in any case would you want to be in an Italian care home?
I've seen two cases recently where the driver in a partnership has become very ill leaving the other member stranded in remote rural areas. I also know of several widows and widowers out here, some have been able to manage well, others have been desperate to leave and not been able to because they can't sell their home here.