Travel and take care of the health

Is there a recommendation for travelers to healthcare in countries with private systems?

I will expand a bit.

I am an Italian citizen and possibly traveled to England, but yesterday I had neck pain and was treated in the hospital of my country with countless illnesses. I'm afraid something similar will happen outside of my country: how would you do it? Is there a common health care strategy when traveling?

I read here that attention in hospitals is free, but I do not know if that is safe / recommended or not.