I didn't mean the educational ethos Andy - more the overwhelming sense of what was right to wear and what wasn't - the quality of it, the colour of it, the make of parental cars on Saturday afternoons visits and what was spoken about in those town cafes ...
That, of course, assumes that all independent schools cater for only that kind of person. The school I went to had financiers' sons, clergy sons, dons' sons, diplomats' sons - yes; but it also had the sons of local and less-local merchants, medics and tradesmen. Iirc, a local journo did a survey of the school shortly after I left, and the two social groups that weren't involved - though probably could have been catered for if necessary - were the A and E bands.
Historically, many of the early grammar schools were established for the edication of those members of society that were not included in the higher eschelons of society.