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?
There are times I opt for private services for speed, because I can afford to, but I could also afford private health insurance (which is cheap in the UK), and haven't felt the need to.
That said, dental is a weak spot of the NHS, with too few dentists offering NHS services, and there's a perceived quality difference in that the NHS treatments have fee caps that mean they will often not include the best aesthetic options. For dental I do tend to go private (but dental for adults is also excluded in quite a few other "universal" healthcare systems - like Norway; don't know about Spain)
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).
> There are times I opt for private services for speed
I'm guessing the NHS, being public, comes with long waiting lists. So it's more about speed than quality of service? I'd assume most doctors with 20–30 years of experience are working in the private sector, right?
New Years Eve, my son was referred to an out-of-hours GP service within an hour of a phone consultation.
But while the shortest wait I've had for a video consultation for myself (via the NHS) was literally 10 minutes, the longest was two weeks.
If you have an emergency, you will be triaged and given a faster appointment if you use the right channels (111 - the non-emergency alterantive to 999/911, or urgent care walkin centres, or A&E as the last resort), but of course many things that are not an emergency will seem intolerable to wait for, and then it absolutely sucks if you can't afford to pay your way to be seen faster.
This is a political/cost issue - the NHS is bargain basement in terms of amount spent per patient compared to many other countries.
A large proportion of doctors in the private sector also works for the NHS, so quality of clinical experience has never been a concern to me.
E.g. when my ex looked for a doctor when she considered having a c-section done private, the top expert she could find was an NHS consultant that worked privately on the side. This is the widespread, and often the private clinics are operated by NHS trusts, as a means to supplement their budgets, and/or the operating rooms etc. are rented from NHS trusts.
If anything, my only negative experiene with lack of experience here has been with private providers (the only nurse that has ever struggled to draw blood from me in my entire life failed to get any blood from me after 3 agonisingly slow attempts where she rooted around in my arm for a vein. Every NHS nurse that has drawn blood from me or my son have been so fast at drawing blood you hardly notice before they're done even when they're filling multiple containers)
But if you want to be pampered, then private providers will be nicer. They're also nicer if you e.g. want more time - GP's are expected to allocate an average of something like 7 minutes per appointment for the NHS patients, for example, and how flexible they will be varies, while with a private GP you can pay for however long appointments you want.
So what they get out of it is at least to some extent that it is expected many places as a means to getting job offers from private providers.
Speaking personally, the biggest issue isn't the waiting, but the chaos and uncertainty. Every part of the NHS is in a constant state of crisis management. I don't terribly mind that I usually have to wait about two weeks to see my GP (family doctor), but I do object to the fact that I'll invariably be seen by a locum (temporary) doctor who doesn't know how the local systems work and won't be there if I need a follow-up appointment. I could live with waiting lists if they were always 14 weeks, but it's incredibly disruptive to not know if it might be 14 or 40 weeks, to not know if your long-awaited appointment will be cancelled with no notice due to staff shortages or industrial action. I've almost got used to the fact that the corridors of my local hospital are permanently full of "temporary" overflow beds, primarily occupied by frail elderly people, often in considerable distress, sometimes obviously neglected.
I'm fairly high-agency and I feel that the system is hostile and difficult to navigate; I have no doubt that many patients who are less able to advocate for themselves suffer preventable deaths because they fell through the cracks.