Private health in the UK can only exist off the back of the NHS.

The doctors are mostly trained in the NHS system. When a surgery happens there's a reasonable chance that it's in the private floor of an NHS hospital, using a private doctor but the rest of the team is NHS. You'll get a private room. But if anything goes wrong, or if you need more after care, you'll be back in the NHS system.

In the UK private health care is at best queue-jumping, but at worst it's poor quality care from doctors who couldn't keep a job in the NHS.

That's a really inefficient way to fund health care. A well run centralized system has massively better buying power and no requirement to provide ever increasing profit margins to shareholders.

I'd prefer my money went to a central budget and was used effectively at a country level :)

Can I also have everyone else in the same boat as me also donate the money they don't need? My few hundred pounds is not going to go far. I don't want them to take just my few hundred pounds. I want them to take in hundreds of millions of extra pounds.

I don't want charities having to rescue people from defunded services that were defunded to give money to people who will never notice it; I want the government to come up with better policies than "let's just cut some more taxes for people who don't need it and won't even notice".

You may feel you don't need tax cuts or won't notice, but don't speak for everyone. You're really just taking the standard position of "I wish the government would take other people's money but I'll phrase it in an odd way, so I can feel virtuous".

The Inland Revenue does accept overpayments. You could give yourself a tax rise and be the change you wish to see in the world. If you don't then it seems like you're not being entirely straight-laced.