I’m an Italian now living in the UK for over 20 years. Perfectly placed to give you a comparison.
If you are Brit looking to move to Italy, I would say the Italian healthcare system is better than the public healthcare system in the UK. Italy spends over 9% of its GDP on healthcare, well above the many other developed countries. One of the reasons behind Italy having one of the highest standards of healthcare in the world.
Of course, there will be wealthlier folk, who prefer more immediate attention, that take out the private healthcare cover.
I hope this helps.