At the same time you can get super-cheap private insurance in the UK because they are effectively a "queue-jumping service" that leaves most urgent and lethal conditions to the NHS and gives you access to private treatments for the things the NHS would put on a waiting list, while cutting their costs by renting excess capacity from the NHS (some private clinics are even run by NHS trusts, as the trusts are allowed to derive some income from private treatments).

I think the best demonstration of the quality of the NHS is that despite the low cost of private insurance in the UK, and despite the fact many companies offer health insurance as a perk, only about 10% of the population has any kind of private cover.