I agree, how can we even have a discussion about some mythical 'right' to healthcare? Hint: It isn't a 'right' if it requires the enslavement of someone else. Doctors and the rest of the healthcare industry are not required to serve you. You do not have a moral claim on their services.
Practically all British GP's run their own businesses. There's nothing preventing them from operating entirely privately, and many do, but most strong to receive NHS payment to take NHS patients because it's well paid and takes all the billing issues out of the equation. A large chunk of British hospital employees also offer private services. Many of them in NHS hospitals, using spare capacity that they can get access to at a low cost, benefitting both them and the public who get some of their hospital costs offset by private providers that way.
Certainly none of them are being forced or coerced, and clearly I must be misguided seeing as I don't know of any countries that force people to become doctors and then force them to work for the public. But I guess that doesn't fit with your fantasy world.
This is the problem with all of the new progressive 'rights' they kee on inventing compared to real human rights. To illustrate, free speech is a fundamental Right possessed by every human being, regardless whether they live in a hellhole that oppresses them.
All rights are human inventions. To pretend otherwise is meaningless.
And all rights are meaningless without at least the possibility of having the means and ability to make use of them. First and foremost that means actually staying alive and in good health. Any society that insists on caring about human rights that doesn't also take steps to ensure that everyone has a recent shot at good health is just plain taking the piss.
This is not a *new* idea - it's an idea that is well over 160 years old, gaining ground starting with the first socialist ideologists, and one that has been penetrating further right in the political landscape ever since (i.e. look at Europe where the vast majority of conservative parties no also staunchly support the concept of a *right* to a level of basic welfare).
Of course since we don't have universal health care you can usually go to an emergency room and get to see someone before you die, unlike the routine horror stories coming out of the British press.
You must be reading different stories from the British press than what they actually publish in Britain. As it stands here, anyone can go to an emergency room and be guaranteed treatment here too, but we don't because the vast majority of us get more than good enough treatment by going to our GP and get referred.
People who are not satisfied are perfectly free to get private health insurance - it's available and *cheap* since they only provide cover above and beyond services where they know they don't stand a chance of competing with the NHS.