Poshness in Private schools? (especially boarding schools)

This topic came up for discussion during my art games option (I don’t do art but I get to do it for my games option at least until the swimming pool opens (the terrors of sub-contracting)). People who go to private schools generally are more arrogant and posh (tweed, polo etc.) It comes from it costing lots of money. This does not mean that they aren’t nice people. Everybody is really nice – but then by about 5th form people started growing up (I had despaired that they ever would) and by the end of 5th form everybody was friendly so the feeling that people might be slightly nicer here than they were at my old school is probably to a significant extend biased by the fact that I am now in LVI. But here you have to live with people every day you don’t want to get on bad terms with them.
I would definitely send my children to a state primary school and then to a school that would stretch their abilities – be that comprehensive grammar or if I can afford it private. I would not however send my children to boarding school until at least LVI unless I really had to and only would at all if they would benefit from it. I go because I did GCSEs which tie into A-levels not Highers (and A-levels are better anyway J).
So I have rambled on long enough I think.