Here in Australia, we have a 2 tier health system. It is usually ranked amongst the highest quality in the world. Everyone has access to free health care but you can also buy private health cover as well, if you want to. We also have reciprocal medical agreements with 11 other countries that cover most medical expenses, if needed , while in those countries. (U.K. is one of them.)
There can still be long wait times for elective surgery and the system is definitely not perfect.
Health care is something all of us will need at some stage, even if its just a visit to the doctor. Why would anyone not want it available for free- or low cost, to everyone?