For the people who have asked how the European system works in practice, here is some more context.
After WW2, Western European countries such as West Germany, France and Austria were in ruins, and everyone had to work together in order to get these countries back on their feet. One of the advantages of the situation was that things could be rebuilt from scratch - not just buildings but also ways of doing things. This was also the case to some extent in the UK, where the Labour government introduced Universal Healthcare through the NHS, despite the medical profession and the Conservatives being against it (and in favour of a US-style insurance-based Free Market model).
One of the key decisions made in the country where I live was that if everyone had to pull together, live through shortages and rationing and so on, then the rewards of the rebuilding programme had to be shared by everyone. In healthcare terms, this meant that the standards of care and treatment previously only available to those who could afford to pay for it should be available to everyone. This is one of the basic principles that still exists today.
What this means is that employees and employers both contribute to the Health Funds (just like UK NI). But - these Funds are ringfenced and the only political input is deciding the level of contributions. Unlike in the UK, politicians have not been allowed to use healthcare as a political football, and not been allowed to let contributions fall behind inflation and the increase demands of the ageing population. Most countries in Europe and the OECD invest more per capita in healthcare than the UK does. For example, Germany invests 30% more every year. Austria has twice as many doctors per capita as the UK - the result is that a GP can be seen just by walking in, there are minimal waiting lists for Consultant appointments or surgery. These countries also had Covid, they also have ageing populations, they also have immigration (at higher levels than the UK has) but still access to healthcare services is totally different to much of the UK.
At the end of the day, England has over 10% of the population waiting for an NHS appointment or treatment. In many places there are no funds available to employ more GPs or nurses, despite the increased demand. The decision to underfund - for staffing, buildings, facilities, systems and equipment - has been a political one. Hunt shafted the NHS when he was Health Minister, and now believes that "balancing the books" rather than "treating patients" should be the priority.
Ultimately, how healthcare is provided in the UK is a decision that has been made by voters. The Conservatives want to drive those who can pay into the arms of the private providers and everyone else can just lump it. Waiting lists get longer. Waiting times get longer. People suffer physically, mentally and financially as they wait for treatment or worry about what might happen if they fall ill. In the 5th wealthiest country in the world, healthcare is increasingly being rationed by price - a situation that is unimaginable and would be totally unacceptable in many other countries in Europe.