I think there should be clarity on the differences between public and private schools.
On one hand, funding for public schools precludes some activities and may result in a lower quality of education due to selection bias. On the other hand, private institutions play by their own rules and this can often result in even worse learning environments.
I don't know what the rules are in the UK (or what they were at the time), but we did get school inspectors visiting from time to time.
I only thought to mention this at all because if you say "public school" in the UK you mean a school you have to pay a fee for, to contrast with "private tuition" (amongst other historical baggage): https://en.wikipedia.org/wiki/Public_school_(United_Kingdom)
On one hand, funding for public schools precludes some activities and may result in a lower quality of education due to selection bias. On the other hand, private institutions play by their own rules and this can often result in even worse learning environments.