An American friend recently wrote a provocative newspaper article that elicited a torrent of online criticism.

No stranger to controversy, she was nevertheless still smarting, the day we met, from one particularly gratuitous insult. "They called me upper class," she said, in her refined but unplaceable Chicagoan accent. "People here are obsessed with class."

Keen Scottish chauvinist as I am, always ready to leap to the nation's defence from international attack, I could only agree, and plead guilty. In this country we are as aware of the distinctions between classes today as ever were the original Downton Abbey generation. If an encyclopaedic knowledge of class nuances, past and present, upper and lower (but with special reference to lower-middle) was set as the entry qualification for Cheltenham Ladies' College or Gordonstoun, I would have been a star pupil.

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In the bright dawn of post-war democracy, when many hoped the ancient class order had breathed its last, it would have been unthinkable that half a century later the way one talks and walks, what one wears and where one holidays, would be as strong an identifying badge of background as soot-stained faces or silk cravats once were. Despite the collapse of the social equivalent of the Berlin Wall, and the creation of a world in which everyone supposedly has an equal chance to get on, upbringing and breeding continue to rear their ugly heads in almost every encounter and transaction. You might argue there is nothing improper or unhealthy about this – but you'd be wrong.

There was a stark reminder last week about how important and divisive social rank is, when headteachers in the private sector put their heads above their well-fortified, immaculately maintained parapets, and complained about being misunderstood and mistreated.

I can vouch for the parapet at Loretto School because it is close to where I live in Musselburgh. The headmaster, Peter Hogan, obviously nursing a long-bottled grievance, bravely aired his annoyance that Edinburgh University appears to be discriminating against his pupils in favour of state-school applicants. This he attributed to inverted snobbery, a sentiment echoed later in the week by the headmistress of Roedean, who has resigned because, she said, it has been hard coping with the constant sense of being "on the negative side of public opinion". At least she might now have an inkling of what it was once like – and in some cases still is – to be working-class and poor.

I cannot speak for the accuracy of Mr Hogan's complaint, although one can't help but reflect that historically the purpose of public schools was not to breed Brains of Britain, but commanders of the empire, whether on the sports field, in Parliament, or in the glistening towers of commerce in Canary Wharf. Parents willing to pay £30,000 a year for a child's education are not seeking intellectual rigour. They could get that at any decent state school. No, this kind of money is seen as a gilt-edged investment, the purchase of a lifetime's worth of connections. If, say, a private school pupil fails to get into further education she or he will not fall into the gutter. In five years' time that child is far more likely to be in a prestigious and well-paid post than the boy from Pollok who got a first in biology from Aberdeen.

That has always been the case, and there's no point bemoaning it. But what is interesting is that the private school sector, possibly for the first time, is raising its voice. I fear we might be seeing the opening of a new front in the educational cold war, because surely only a sense of embattlement would make such elite bastions go public with their problems.

In these straitened times, pressure to get into the best universities and jobs is growing. Regardless of a lowly background that would once have rendered them invisible, talented young people are winning academic places and posts ahead of privately educated peers. As recession bites deeper, and the gulf between the rich and poor widens, the issue of background, and of the privilege that money buys, looks set to escalate rather than be buried, like the shameful anachronism it is.