I'm not so sure it's as bad as the media make out, TBH (apart from all the waste).
My doctor's surgery irritate me because they won't allow me to book non-urgent visits to my GP in advance. If I phone them, they insist on giving me an appointment later that day or next day, when there's insufficient notice to arrange work commitments around it.
Pharmacies
are taking an increasing workload from the NHS. My local chemist has offered me NHS flu jabs while I've been collecting prescriptions the last couple of winters, saving an appointment at the surgery, and they can now carry out reviews for certain conditions, again, saving an appointment at the surgery.
I agree that those who are no-shows at surgeries, or present for time-wasting reasons, should pay a penalty. It should be free at the point of use to those who don't waste resources, however.
Both of my parents have had episodes requiring surgery in the last 3 months. In my Dad's case it was not life threatening but completely debilitating. He was operated on the day after presenting himself at casualty. In my Mum's case it was potentially cancer (but thankfully didn't turn out that way) and she got various scans, a biopsy then straight into Guy's for a major operation within a couple of weeks.
I don't doubt that some are failed by the NHS, but I've yet to personally experience care that could be improved in any way, TBH.
It does come at an enormous cost, of course, and, like most things in the public sector, the government risk a huge revolt if they dare to try to make it more efficient.