"True to an extent, but you can hardly compare the difference in quality between some state schools to each other to the inequality fostered by the private system to state."
I'm not sure about that OP. I think you have a rose-tinted view of 'private schools' tbh, as they vary massively. What kind of 'pruvstr schools' are you talking about? Some are 'money for old rope' frankly, run by eccentrics and people with a business mindset, rather than an educational background.
Any school, state or private, is only as 'good' as its catchment / intake. The main difference between schools is determined by location (if a school is non-selective) or, as is the case with most private schools, how academically selective it is at 7+, 11+, 13+ etc. What is the difference between a school like Brampton Manor (state) and other schools in that area? Nothing, except the former is highly selective and can take pupils from out of catchment.
We have various friends who live out in Surrey, Berks etc and the state schools are great. In London, things are much more variable. There is one state school not far from here with a very small catchment which consists predominantly of houses worth £3m upwards. Those families are wealthier than most families elsewhere who use private schools. Of course that school is going to be seen as 'desirable' - they don't have to deal with the social issues that the next comprehensive school (down the road) have to deal with because that school happens to be located next to a large housing estate. As I said, in London, it's very often 'selection by postcode.'
Teachers are teachers, there is good and bad in all schools. But of course, in any selective school (whether selection is by academics, ability of families to pay fees or by location / postcode), teachers will have an easier job and be able to focus in the job of teaching.