SJane not really. My guess is that DD is not used to having much disposable income, which is what she has in common with her University friends. Our income was largely swallowed up by mortgage, transport, childcare and school fees. A shabby house, cheap gite holidays, and an elderly car did not bother us. DC knew several children of billionaires. They learned that deprivation comes in many forms: lack of parental attention is one, lack of personal safety is another.
There is a lot of wealth, or more accurately casual spending, on display at University. Kids able to hang out in trendy coffee shops, buy toiletries from places other than Lidl, go out several times a week, buy train tickets at the station rather than in advance, drugs, and so on. Private education or not, this is not DDs background. A much higher proportion of London DC go to private schools. In some boroughs it is over 50%, and so she is not unusual. There are some real education black holes, where housing is cheaper, and so middle income families have a three way calculation on how disposable income is divided between mortgage, school fees or transport. Spend less on one and you are likely to spend more on the others. There is no obvious reason why she should suddenly decide to hang out with the posh boarding school girlies at University, similar to those who used to invade the London party circuit a weekends, when she never mixed with them before.
London private school teachers are in a similar position. If they are lucky the school provides accomodation but it is still a juggling act. I doubt that they prefer the rich kids over grounded pupils with hard working just-about-managing parents.
Worth noting is the advice from an American friend when I was being patronised horribly by a snobby Kensington mom. For many London expats the lifestyle comes with the job. The smart house is rented, the car is leased, the school fees are paid. The job goes, everything goes. I am sure schools realise that public sector job security and (scruffy) house ownership is more substantial.