I think there is some confusion here over the difference between public/ private schools.
And I must admit I'm not 100% myself!
I went to private schools. That is paid for but they come in various types.
My primary was a Roman Catholic school (with nuns!) In London. If you paid you went. Large numbers of children of Irish and Italian descent who wanted a Catholic education for their children. Academic standards were not great or anything.
Secondary I went to a selective private school. If you passed the exams and got in and your parents could pay you could go. A reasonable mix of children who had parents who were doing well enough and saved up- some children who were super talented at eg music got bursaries etc. My classmates had parents who were teachers, nurses, that sort of thing. Plus some wealthier business types. I suspect that it's out of reach of those occupations now but it's all, if you get in and can pay then ok.
Public schools are different entirely. They have a whole different set of entry ages for a start. I think you go to prep school till 8 and then move on to senior. Prep schools are expensive obv. So already it's out of step with state and private schools. It's a different system..
My brother went to a public school on a scholarship. Most children boarded (another thing that seems to be the standard at public schools). My brother was a 'day boy'.
It was really really posh, massive and different even to me as a private school girl. Just a totally different ball game.
And here I get a bit guessy. I would imagine that if you were the child of a lord of something, you could go irrespective of academic achievement? Others may no more. To me though they're about social position and mixing with others in a similar social position in a money no object type place. Of course many get excellent results etc.
I mean my experience is limited but public and private schools are totally different.
From my point of view which I know will be unpopular.
The tax breaks given to these schools as charities (at least the private ones, I don't know if public are set up that way) are ridiculous.
There's no doubt that public schools serve the privileged to funnel their children through well trodden routes to various positions.
There was a lot of to and fro about grammar schools and whether they were a good idea. I can see the arguments against but having seen a documentary a few years back, removing the grammar school system, rather than bringing more equality, simply meant that there were very few people breaking through that class divide at all any more.
I would be supportive of a comprehensive system across the board and get rid of being able to buy an education. It's inequitable and creates a two (in our case 3) tier system.
Having all the children in state education would focus on improving standards there and mean a more level playing field.
I know that this is controversial and never going to happen! But just putting it out there.
I also think that it's not good to have so many religious schools. Again, another conversation.