Perhaps we should be looking more closely at the Finnish system*
The Finnish system is screwed, falling down the rankings due to bad curriculum decisions. No one is looking at it any more.*
This times a hundred.
I was educated in the Finnish system when it was world leading (left high school some 15 years ago). It was a traditional teacher-led way of learning and it focused on a wide range of serious subjects across humanities & sciences. We started at aged seven and started pretty full on, homework and expectance of a strong work ethic were very much part of it. Exams were left for teachers to manage locally, the first national exams didn't take place until I think aged 15/16. So teachers were trusted to do their job well.
Once politicians started "modernising" it, it's gone massively downhill. They no longer seem to believe in teachers teaching, they should now just "facilitate" etc. All that stuff...
As for abolishing private schools in the U.K., I'm uncomfortable with the idea of private education, but I also know that in the end I am more than likely to end up paying for schooling in the U.K. Either through inflated property prices within a good school's catchment area or, more directly, through fees. I'm fully aware that I'm hypocritical in this matter, purely driven to do what I believe would be best for my kid & within my means to offer.