The headteacher of a UK public school is under fire for likening criticism of the private education sector to antisemitic abuse.

Anthony Wallersteiner, of the £12,000-a-term Stowe school in Buckinghamshire, also said a decline in the number of non-state school Oxbridge admissions had left some parents making claims about “social engineering”.

He told the Times: “The rise of populists and polemicists has created a micro-industry in bashing private schools.”

Wallersteiner, who is of Jewish descent, 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 that the Jewish minority was over-represented in key professions: medicine, law, teaching and the creative industries.

“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.”

Dame Margaret Hodge, who was at the forefront of highlighting allegations of antisemitism within the Labour party, described his comments as “insulting and outrageous”.

She told the Press Association: “It’s insulting to all the young people who have secured places at Oxford and Cambridge on the basis of hard work and potential. And it’s insulting to the victims of antisemitism to compare the two.”

A spokesman for the Campaign Against Antisemitism said: “Tasteless Holocaust analogies do not belong in the debate about education in this country. Nazi propaganda against Jews was used to generate public support not only for exclusion from education but also for brutal beatings, boycotts, degradation and eventually the mass murder of 6 million Jewish men, women and children.”

Wallersteiner told the Times that many parents had been complaining about positive discrimination and their children being edged out of Oxbridge.

“There’s a much more concerted effort by [Oxbridge] admissions tutors to drive down the number of places given to independent schools and redress the balance and to put in contextual details,” he said.

Boarding fees at Stowe school are £12,697 a term. Photograph: Chris Radburn/PA

His comments triggered a furore on social media, with some commentators suggesting his position had become untenable.

Stephen Pollard, the 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.”

The Labour peer Andrew Adonis said: “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?”

Wallersteiner has robustly defended the private school sector down the years, often making provocative comments. Two years ago in an interview, he said: “Giving the independent sector a good kicking has become a national sport. Barely a week passes without a well-known public school being lambasted in the press for some real or imagined indiscretion.”

Wallersteiner’s latest comments have invited further scrutiny of the Oxbridge admissions process, with many experts pointing out there has been only a negligible rise in the number of state school pupils in recent years.

Analysis by the Sutton Trust, a social mobility charity, published in December showed that eight private schools sent 1,310 pupils to Oxbridge over three years, while 2,894 other schools sent 1,220 students between them over the same period.

In 2017, 64.1% of students at Cambridge were from state schools, compared to 61.4% in 2013. In the same period at Oxford, the figure rose from 56.8% to 58.2%.

The Labour MP David Lammy tweeted on Friday evening: “A 1.4% rise in five years in state school kids getting into Oxbridge and the parents of private school kids fear social engineering! Is the Times having a laugh? That’s 40 kids per one college.”