David Fletcher, Stowe’s registrar, resigned this week over comments made to The Telegraph reporters posing as representatives of a Russian oligarch who wanted his son to study at the school.

“It is not just British pupils that may have been cheated out of places, but overseas pupils too”

Covertly filmed footage showed Fletcher saying a hefty donation could tip the balance if there was a “marginal decision” over whether or not to admit a student.

He described being approached on multiple occasions by Russian agents offering to “work with” Stowe – which he calls a “code” signalling a donation in exchange for a school place.

“We are pretty straight, we say look here, they have to be able to pass [the entrance exams]… but if that’s the case, there is no reason why they shouldn’t go all the way through,” he related.

Fletcher added: “It’s a big growth industry, because, as private education prices itself out of the market with British families, many schools are having to go down that international route to stay afloat.

“I always say to my headmaster – he’s terrific but in some ways he’s a bit naive – I say to him you just don’t realise how things operate elsewhere… and also you don’t understand that some of these people are rich beyond Croesus.”

Fletcher has since resigned over his “inaccurate and inappropriate statements”, Stowe said in a statement.

Two London-based education agents also said that donations could help secure places, according to the The Telegraph.

One told reporters that at one high-profile school, “if there is an opening to be exploited I know those guys, they’re ruthless and they will push for [£5m]”.

Former Shadow Education Secretary Lucy Powell MP has called for the revenue service and the Charity Commission to investigate whether the practice is more widespread.

Despite the revelations, Alexander Nikitich, founder of Carfax Education Group, which places foreign pupils in elite UK schools and universities, told The PIE News he believes “it is only a few schools that had given in to the temptation of easy money”.

“It is only a few schools that had given in to the temptation of easy money”

However, he is concerned that the incident may affect attitudes toward foreign pupils.

“Some British families may feel, and in law may have been, defrauded of places they should have got on merit, but that were sold for donations instead.”

“The truth of course is that it is not just British pupils that may have been cheated out of places, but overseas pupils too,” he said, adding that at some schools, “If you are from Russia or China, the immediate assumption is that your parents are billionaires and they have to give money to the school.”

Responding to concerns British parents may have, a spokesperson for the Independent Schools Council stressed that overseas students are not “rapidly filling independent schools”, representing just 5.3% of all students in 2016 compared with 4.4% in 1982, according to its census.

“If parents of pupils wish to make donations to schools, it is common practice for senior academic staff, including heads, to be unaware of the source of the donations in order to ensure it cannot affect decision making about individual pupils,” they added.