In theory all the costs are covered and there would not be a need for supplementary coverage. The systems in the UK and Canada are what we in America would call socialized and are paid for from mandatory taxes. I never was able to get an exact figure but I'm guessing the taxes into the National Healtcare System would at least be equivalent to what we pay for insurance. The UK also has private healthcare which any citizen may opt into. Unfortunately that does not relieve them of the tax for NHS but it does provide non-socialized healthcare.The sad thing is, because medicine is socialized, they can't go out and buy supplemental insurance as we can here.
You have pointed out in the past how the cost of healthcare increases far beyond the normal rate of inflation. It's hard to imagine all the forces in operation to account for that, but I do think they are on the cutting edge of science. Somebody has to pay for all that research. Ask any pharmaceutical company about it. They will explain it eloquently.