On the NHS, I tried for years to push for improvements to switch to digital cancer screening invitations after they missed my mother (offering to build the software for free), which is now happening, but suggesting the NHS isn't perfect is against the religion here. My sister who works in NHS DEI hasn't spoken to me since publishing a book on it.
Every time someone with the finances, vision and ability leaves I think the situation gets a little bit worse, it increases the proportion of people remaining willing to put up with all of it. Anecdotally, many of my friends have already left, some of the older generation want to leave but feel tied in. My flight out is in 6 weeks. Good riddance, no doubt.
That's really not my experience. In fact, almost everyone is surprised when I suggest that despite its many problems, the NHS does better for the people than most modern countries' health systems.
No one I know who has lived in France or Germany or any developed country other than the US thinks the NHS is better than the systems in those countries.
I'm not entirely sure if the UK has a public-private health system. What I do know is that companies offer private health insurance, even though everyone has access to the NHS. That suggests there's a private system in place, one that probably attracts the most experienced and competent doctors and GPs?
E.g. my old GP used to provide both private and NHS services (they were precluded by their NHS contracts from providing private services to people registered with them with the NHS).
Many NHS trusts also provide private services, as they are allowed to do so to improve utilisation and supplement their budgets, so in practice this is part of the reason the NHS is so cheap compared to universal systems in similarly rich countries.
Most private hospitals in the UK also e.g. rely on NHS for intensive care, and this, along with relying on the NHS for first-line care (A&E, GP's unless there's a wait, etc.) is also why private health insurance in the UK is unusually cheap, and why private hospitals in the UK are unusually cheap (if you're in the US, and planning elective treatments, it can be cheaper to fly to London and do it here, even factoring in hotels - and some Central London hospitals have hotel suites, and at least one have or had a previously Michelin starred chef because they cater - literally - to high-end international healthcare tourism).