My school is nowhere near the poshest private school. I'm the only one that talks posh, everyone else has a neutral Midlands-ish accent. I would say about a third of children came from state primary schools, a third came from the junior school connected to our school, and a third from posh prep schools. The thing is - among the non-popular girls - no one really gives a cr*p whether you're posh or not posh or rich or poor. My friends are basically the nerdy kids, and a good half of us are on scholarship or bursary. I am myself. This has affected NOTHING - except to give me higher social standing amongst the nerdy kids! Scholarship doesn't mean you're poor, it means you're smart. Embrace that!
Alternatively, if you prefer to seek your friendships amongst the popular girls, prepare to be judged horrifically on whether you're wearing Jack Wills, whether your house is a mansion and whether Daddy has a jet plane and a villa in the Seychelles. The less brands, money and class you have, the lower social standing.
Further alternatively, if you wish to get in with the popular boys, all these things are completely irrelevant. To make friends among this set, you need a nice body, a lack of morals and something which we call 'banter'.
Have fun!