An elite boarding school is one of 50 British education providers to have received fees via tax haven companies that were customers of a now defunct Lithuanian bank, according to data from one of the largest ever banking leaks.

The disclosures come after ministers specifically warned private schools to undertake better due diligence over the sources of fee payments.

Charterhouse, in Surrey, describes itself as “one of the great historic schools of England”, espousing “sound Christian values”. Established in 1611 on the site of a monastery, it has educated some of the giants of public life, including the poet Robert Graves, the broadcaster Jonathan Dimbleby, and 200 years before him, the evangelical preacher John Wesley. The foreign secretary, Jeremy Hunt, is a former head boy.

Today, it welcomes children from around the world. Among them, in 2010, was a boy with a Russian name whose family chose an unusual method of paying for his education.

Over the course of one summer, and three separate transactions, Charterhouse collected five years’ worth of boarding fees. The payments, totalling £300,000, were wired from a bank in Lithuania to the school’s account at Lloyds in Godalming, Surrey.

The money did not, as might be expected, come from an account in the name of the boy’s parents. Instead, it was paid by an anonymously owned company registered in St Lucia called Meister Developers Ltd.

The details come from one of the largest ever leaks of banking data – 1.3m transactions involving 238,000 account holders, most of them shell companies that were customers of different Baltic banks. Most were clients of Ukio Bank, which was closed by regulators in 2013.

The leak is called the Troika Laundromat, because more than 70 of these offshore shell companies were operated by staff at an independent private banking arm of the Russian investment bank Troika Dialog.

Some of the payments to schools came from companies operated by this division of the investment bank. Others, like the money for Charterhouse, came from shell companies unconnected to Troika.

British schools, colleges and education consultants received more than £3m from account holders featured in the leak, according to analysis of the data by the campaign group Transparency International UK.

“There is growing evidence that educational institutions across the UK are receiving funds of questionable provenance,” said Rachel Davies Teka, of Transparency International.

“It’s crucial now that the sector stops burying its head in the sand and faces up to this problem by flagging any suspicious activity to the authorities.”

All of the payments were from opaque shell companies whose ownership was obscured by tax haven secrecy, or the use of nominee directors and shareholders, making the source of funds difficult to establish.

There is no suggestion schools did anything wrong or accepted illicit funds.

However, the government has warned businesses and services providers to carry out better checks.

“We need to go after the people who have not played their part in hardening the environment and reporting,” the security minister Ben Wallace said in a recent Guardian interview.

“So the purveyors of luxury goods, the public schools, the sporting institutions, who don’t ask many questions if suspicious people come along with cash or other activities, we will come down on them.”

Meister Developers, which transferred the cash to Charterhouse, pumped hundreds of millions of dollars through Ukio. Many of the transfers seem to be related to normal business transactions. However, in 2006, Meister appears to have accepted more than $60m of payments, which can be traced via court filings to a fuel price-fixing scam at Moscow’s state-owned Sheremetyevo airport.

There is nothing in the data to suggest the boy’s parents were involved in the fraud. Meister appears to have been part of Russia’s grey banking infrastructure, according to one anonymous source who received payments via the company. It was a vehicle for sending cash to Europe, and its operators offered this service to many different and unconnected clients.

Charterhouse said records for 2010 were no longer kept and the staff involved were no longer at the school.

“In 2010, there was nothing in the public domain about Meister Developments [sic] to raise our concerns, and there was nothing we knew of in the family situation to arouse suspicions,” the finance director, David Armitage, said.

“The son joined the school immediately after payment was made. Government guidance has now been updated and we hope this will help schools to be ever more informed and vigilant.”

Lancing College was paid more than £75,000 by Troika-administered Castway Management Ltd, registered in the British Virgin Islands. The payments began in 2007 and continued into 2010. The pupil’s father appears to be Andrey Kislov, who has been an elected member of the regional Duma for Samara since the 1990s. He is also the general director of Gazprom Mezhregiongaz, a subsidiary of the state-owned gas company. Kislov did not respond to a request for comment.

Lancing said its files show checks were carried out “in accordance with the standards of the time” and revealed nothing irregular. The school said that, given better awareness of money laundering in the current climate, it had reviewed its procedures and was about to review them again “following Ben Wallace’s recent comments”.

The pupil’s sibling apparently boarded at Oundle school, which in 2011 and 2012 banked more than £30,000 in transfers from Airship Universal Inc, a screen company administered by Troika. The school said sources of fee payments “are of continuing concern to independent schools”, and that its processes were updated last year.

Ruben Vardanyan, the owner and chief executive of Troika Dialog, chose Hill House for his children. Located in Kensington and Chelsea, its former pupils include Prince Charles and the singer Lily Allen. Ukio Bank recorded $40,000 in 12 separate payments to an account in the name of the London school. They were all sent from Quantus Division, which transferred $700m out of Ukio accounts over a six-year period.

Vardanyan did not deny the fees had been paid from Quantus. Richard Townend, the school’s headmaster, said: “I think you may have the wrong Hill House. We do not and never have accepted such payments.”

Townend did not respond to a question about whether the account at Coutts bank that received the funds belonged to the school. The sums paid correspond to the school’s published fees in 2007 and 2008.

Mike Buchanan, who heads the Headmasters’ & Headmistresses’ Conference, which represents heads from leading independent schools in the UK, said his members were “acutely aware of their duties to help uncover illicit wealth”.

“The sector has worked hard with the Home Office to ensure that guidelines have tightened up in line with current legislation, and every school now has an updated procedure to help them check the provenance of funds,” Buchanan said. “For example, it is not uncommon for parents to gain good rates by paying fees in advance, but if such a payment came from an unusual source, or at a surprising time of year, this would now attract scrutiny.”