@taxguru
As my post suggests, I have experience of European healthcare - I've lived in several EU countries.
The UK has private providers of healthcare insurance that are non-profit (in the sense that they make a profit but re-invest this in the organisation and don't have shareholders). BUPA would be one, but BUPA only has one hospital and 50 health clinics - i.e it has cherry picked the services it will provide. These "non-profit" insurers also cherry-pick their customers, refusing to cover for a number of pre-existing conditions or setting premiums so high that they are unaffordable if a condition is diagnosed. BUPA's hospitals were sold to Spire several years ago. Spire is a FTSE 250 company, so is definately run to make a profit.
Nuffield Health as a healthcare provider is registered as a charity and notionally a non-profit organisation, but only provides treatment against payment - either the patient pays directly or their private insurance covers the cost. In the European scheme, a provider such as Nuffield would participate in the universal healthcare system by also providing treatment at a fixed, agreed cost to Krankenkasse patients, as in the hip replacement example in my post. This cost would be the same as the Krankenkasse would pay any other provider for the same treatment, be that a public hospital or a private (either profit or non-profit) provider. Many people in the UK seem not to understand how this system works, or how it differs from the American system.
I'm in complete agreement with your main point - that if people are unwilling to consider other forms of healthcare delivery (aka NHS reform) then the UK will sleepwalk into the American model - which is what many "low tax / small government" politicians would like to see, and what some very wealthy and powerful American companies have been lobbying for for many years. They see the UK health service as one of the last golden opportunities to milk a cash cow.