At Westminster School, the 500-year-old institution opposite Parliament where a huge proportion of British thinkers, academics, artists, actors, politicians and military leaders were educated, there is a tradition called the Greaze.

Since 1753, for reasons lost to history, the school assembles in the large hall on Shrove Tuesday, and the head cook throws a horsehair-reinforced pancake over a long bar, his accuracy improved by the customary threat of being stoned with Latin primers, or "booked". Pupils fight to grab the largest piece of the pancake for a cash reward.

Originally the whole school was involved, but the custom had to be downscaled because of deaths. This school – which also squeezes some of the best A-level grades in the land out of even its least promising fee-paying pupils – has educated a disproportionate number of British government members, including the current Deputy Prime Minister and several front-benchers. That fact alone should tell you a great deal about how power and privilege continue to work in this country.

Private schools are being debated again, after the Education Secretary Michael Gove gave a speech at Brighton College – my old school – which has just been named Independent School of the Year. In that speech, he laid out a shaky case for his academy programme before reminding the fortunate gathering just how many prominent people in politics, business and the media were educated privately.

He made a particular point of naming and shaming left-wing journalists – including myself. In the eight years since I left Brighton College, hundreds of people, most of them right-wingers, have suggested that the fact that I went to a private school and then to Oxford places indelible inverted commas around any radical sentiments I may espouse. That notion – that there is some element of hypocrisy at play if "radical" journalists have been to private schools – betrays an important prejudice.

In the world of inherited wealth and privilege which people like Michael Gove exist to defend, money and class are more important than ideology, and everyone is divided up into warring tribes based roughly on how much money their parents have. It follows that whatever your professed values, if you come from a fortunate background, you must secretly wish to further the interests of the class in which you were born. The idea that nobody can really be a socialist if they were lucky enough to go to a private school is wilful stupidity – and yet, and yet, and yet.

It would be just as nonsensical to claim that going to Brighton College, on a large scholarship and carrying the expectations of my state-school-educated family, did not have an enormous material effect on the course of my life. For instance, in 2003, I was informed by a teacher that I would be applying to Oxford. I was the smartest kid in a smart school which needed to boost its Oxbridge figures: there was no question. The only trouble is, I was shy, had a stutter and a tendency to twitch. So a teacher was roped in to practice the interviews with me, to teach me to speak more clearly and be confident in my ideas, to act– I'll never forget this – as if I had a right to be there.

Would I have got to Oxford, or become a journalist, without Brighton College? Impossible to say. But this year when, yet again, around 50 per cent of Oxbridge undergraduates will be chosen from a private school system that educates just 7 per cent of the population, I won't be surprised. What private schools instil in their pupils is more important than a satchel of perfect GCSEs: it's what the philosopher Bourdieu called "social capital". It's poise, self-respect, and the unshakeable belief that doors will open for us, that when we speak people should listen, even if our hands are sticky with pancake-grease. Meanwhile, decent teachers at state schools fight to spend enough time with kids to encourage them to raise their voices at all. Is it any wonder that so many British commentators are privately educated?

The British private school system is one of the most perfect machines for perpetuating privilege ever invented. It is a marriage of extreme convenience between the ancient functions of the landed gentry and their aspirants – pomp, ceremony, self-satisfied elitism and a masochistic dedication to various savage field-sports – and the reptilian efficiencies of the market.

Private schools, as Gove warmly noted in his speech, can pay to attract the best teachers, to have smaller class sizes. Liberal parents who can afford to educate their children privately face an occasionally agonising choice between abandoning their values or abandoning their children to overstuffed, under-remunerated state schools. Those who make that choice, or benefit from it, gradually learn to make excuses for their own purchased privilege – to learn the language of their new team. And that's how they get you.

Any Education Minister who was remotely serious about tackling educational inequality in this country would start by removing the tax-exempt status of British private schools, with a view to dismantling them altogether – but Gove has no interest in doing that. He was simply reminding the pupils of Brighton College of what they learn, in my experience, every day. He was reminding them what team they're on.

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