Well, yes, PortAndLemon, I was thinking that too. Presumably neither were particularly indicative of state school/private school.
Certainly where I live, many state school pupils are just as 'posh' as the private school one in the prog, but hopefully without her attitude.
The 'attitude' unfortunately DOES come from only mixing with a certain strata of society. It wasn't really about 'schooling' it was more about their parents I think and obviously the different opportunites available to children nowadays (ie nil to child on sink estate, everything to child in richer area). I think it did serve to actually make posh child realise that she is actually privileged, which IMO, many private schooled children don't actually realise, as they live in such a bubble of PLU (people like us).