It was Stowe’s first headmaster, JF Roxburgh, who suggested the school should aspire to produce students who would prove “acceptable at a dance and invaluable at a shipwreck”.

On Saturday, though, the current head expressed fears that these days, his charges were more likely to find themselves victims of social engineering, which he equated with antisemitism. In explosive comments about attempts by Oxbridge to raise admissions from state schools, Anthony Wallersteiner likened the treatment of private school pupils to the Nazis’ persecution of Jews.

The head of the £12,000-a-term Buckinghamshire public school told the Times that “the rise of populists and polemicists has created a micro-industry in bashing private schools”.

Wallersteiner, who was educated at the King’s School, Canterbury, said: “Some of the criticisms echo the conspiratorial language of The Protocols of the Elders of Zion. It was relatively easy for Hitler and his henchmen to suggest the Jewish minority was over-represented in key professions: medicine, law, teaching and the creative industries.”

The headmaster of Stowe, whose alumni – known as Stoics – include David Niven and Sir Richard Branson, originally laid out his thoughts in a lengthy, unpublished article seen by the Observer in which he acknowledged “it is not hard to understand why there is a general perception that independent schools are unfair”, given how few privately educated pupils come from poor backgrounds and receive free places.

Elements of the original article, which included the Elders of Zion reference but not his comments on the need for private schools to do more to improve social cohesion, were included in the Times’s piece, along with additional quotes from an interview Wallersteiner gave the paper.

“There’s a much more concerted effort by [Oxbridge] admissions tutors to drive down the number of places given to independent schools,” he told the Times. “Privately educated pupils in the UK are also being accused of dominating the top jobs and stifling social mobility … it is all too facile to stereotype groups and ignore the fact that lawyers, doctors, writers and politicians are individuals.”

The comments caused a furore, with calls for him to step down. Stephen Pollard, editor of the Jewish Chronicle, tweeted: “Clearly the headmaster of Stowe is not an idiot. But he is doing his best to convince people that he is. And his words are so appalling that I doubt he can stay.”

Labour’s Lord Adonis said on Twitter: “If the headmaster of Stowe believes his students are treated by university admission in the way Hitler treated the Jews, why does he think their parents pay £39,000 a year for the privilege?” A spokesman for the Campaign Against Antisemitism said: “Tasteless Holocaust analogies do not belong in the debate about education in this country.”

Stowe School, in Buckinghamshire, charges fees of £12,000 a term. Photograph: David Goddard/Getty Images

Some commentators pointed out that Stowe’s academic performance was comparatively poor, especially given its considerable fees. Labour’s Margaret Hodge, said: “These preposterous remarks are not just ignorant but offensive – offensive to those who have secured a place at Oxford or Cambridge through their hard work and ability, rather than size of their parents’ bank balance, and offensive to victims of antisemitism.Hopefully anyone sending their children to Stowe will now reconsider and stop denying them the privilege of a state education.”

Wallersteiner remained true to Stowe’s motto, Persto et Praesto – “I stand firm and I stand first”. A spokesman said he would not resign.

Wallersteiner has offered a robust defence of private schools in the past. Two years ago he complained that“giving the independent sector a good kicking has become a national sport.” But his latest defence is unlikely to help its cause.

“It seems that the private schools are determined to cut their noses to spite their face,” said Robert Halfon, Tory chairman of the education select committee. “This comment is the trivialisation of real evil. Private schools should do much more to help those from the most disadvantaged backgrounds.”

Kate Tunstall, a senior academic at Oxford University, said:“There is a long and very ugly history of using antisemitism as a metaphor,” she said. “As teachers, we should be tackling it, not exploiting it, and tackling all forms of social injustice, including educational disadvantage.”

The row has renewed the focus on Oxbridge’s record on social mobility. In 2017, 64.1% of students at Cambridge were from state schools, compared with 61.4% in 2013. At Oxford, the figure rose from 56.8% to 58.2% over the same period.

Olivia Taylor, 19, an undergraduate at Cambridge and former state school pupil, who used to qualify for free school meals, suggested the rise was good news for pupils from all backgrounds.

“If you go to a private school, people believe in you from a very young age, you grow up working to get here – and if it’s slightly harder for you to get in now, you should see that as a positive thing, because it’s a step towards your entry being based on merit, not privilege.”