On one of the adult education creative writing classes I have been to, the tutor was a teacher from a very expensive and nationally respected private school in my area which has really impressive facilities.
She was the most boring, unimaginative adult education teacher I have ever had. Conversely, one of the best creative writing courses I have been on was run by a former state school teacher, turned teenage fiction writer.
If a school has, for instance, theatres, state of the art laboratories, extensive grounds and sports facilities, etc., this must have some effect on pupil attainment. Some private school teachers may be excellent but then so are some state school teachers.
I think charitable status should be withdrawn from private schools. They are businesses, not charities, and any measure to make their charitable status more acceptable would be, in my opinion, just window dressing. With the increasing number of private religious schools, I wonder if the cost of monitoring that their curricula, teaching practices, etc., are in line with accepted standards, is paid for by the school or by the state.
Recent newspaper reports suggest that the vast wealth of overseas oligarchs is responsible for the massive rises in private school fees, to such an extent that even highly paid professionals are increasingly unable to pay the sorts of amounts that are now being demanded.