My own brother got his ear pinned back when he was a teenager because he was being bullied about it at school. Cost nothing and happened within a couple of months of GP appointment.
And obviously being a highly developed western country you can find private clinics for just about anything you want.
I have my own experience with this, I was/am a heroin addict and it took 12 months to get into any treatment at all. And A&E wait times are increasing year on year, either this winter or next there is going to be a crisis. Already we’ve come close.
I still maintain that for the vast majority of people and ailments the NHS is perfectly adequate, it’s just hobbled by the government at the moment. You could conduct a poll of almost any demographic in the country and they would say they would be willing to pay more taxes if they were ringfenced for the NHS.
Which advanced procedures aren't available in the EU? By the way, you can find private clinics in most EU countries if you don't want to use public health providers.