Couldn't not chip in!
I went to a private school and so did my bro.
There is a huge difference between schools, some are cheaper some cost the earth, some have mechanisms whereby children mix with others some don't, some are based more in communities and some aren't.
My brothers school was very expensive and very posh. Set in the country with rolling acreas etc and was boarding and day. More of the idea of a public school I suppose. You didn't have to be as acaedmic to go there.
My school was extremely acadamic and an awful lot cheaper. When people say "people from all backgrounds" of course that is rubbish but it's not all multi-millionairres. A lot of the parents in my class were "in business" whatever that means or teachers. Yes they obviously had a reasonable income but not staggering wealth.
I went to a state 6th form and settled in easily.
The interesting thing is that my brother is about 15 times posher than me! While I have a local accent my bro talks like he has a plum in his mouth. He doesn't mix with a huge range of people whereas I do.
But then we have very very different personalities as well.
I think to say broadly that all private school people end up like my bro is way too general. I have met people from posh areas with state educations who have never met/mingled with anyone outside their social group either (it is a real bugbear of mine).
I also think that "life skills" wise I learnt many things at a private girls school which my state friends at 6th form didn't know about - at school about 70% of my class had eating disorders, there was a lot of unerage sex and drug consumption was fairly high. It's not all sweetness and light in the private sector either.