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just to add, I think church schools should be abolished before generic private schools.
I don't think the general population would be willing to have an appreciable rise in council tax to facilitate this if implemented all of a sudden.
Faith schools are part funded (10%-25%) by the church/synagogue/etc that they are linked to. The children they educate would still need to go to a school so if this funding disappears the Government have to make up the difference or they have to find new schools in the same area (which generally there aren't).
Also, many of the faith schools are on land not owned by the local authority. There would be a huge real estate bill to buy it to run a non-faith school on the same site.
The government are dealing with this (slowly) in that any new faith school being built is capped at a maximum of 50% faith entry. I can see this slowly being increased over time to eventually separate faith and school. (See: https://en.wikipedia.org/wiki/The_50%25_Rule)
(Disclosure: My daughter goes to a faith school so I'm not entirely impartial, however as an atheist myself [my wife does the religion bit] I'm often surprised at what people seem to think goes on in a faith school. There is no creationism being taught.)
I went to three private schools, primary school then gcse years then college years. First was alright, second was generic rugby, lads, bully etc. third was really good. I think I'd be a bricky or something now if I didn't have someone being paid to push me for better grades because I sure as fuck wasn't getting that at home.
I agree in principle that private schools should be abolished and the money should go to all the state schools instead but also I severely mistrust the govt to actually give the money to the schools. I think I ended up in them more due to availability than any sense of snobbery, we moved from one end of the country to the other and it was a real struggle to find schools for my sister and I. Obv we could afford it which was nice but we weren't rich, the money came from my grand parents.
I know there's no way I will be able to afford it but I would 100% send my kid(s) to private school if I could mainly for the better access to sports and facilities.
edit - just to add, I think church schools should be abolished before generic private schools.