The competitions watchdog has issued a strongly worded warning to private schools in the UK, threatening hefty fines if they are found to be price-fixing during the coronavirus crisis.

The Competition and Markets Authority (CMA) said it had been made aware that a number of independent schools “may be engaging in discussions with each other about the level of discounts and/or refunds on school fees”.

A letter from the CMA to the Independent Schools Council and other bodies representing the sector warned that moves to agree prices and exchange commercially sensitive information would almost certainly infringe competition law and could result in fines of up to 10% of total turnover.

Independent schools have been badly hit by the fallout from the Covid-19 pandemic, with some parents who have lost work unable to pay fees while others are reluctant to pay the full amount for the online education schools are currently providing.

Many schools have already offered discounts and refunds to try to keep families onboard and stay afloat. While the bigger, more established schools will most likely survive, there are fears that smaller schools, which may have already been facing difficulties, will go to the wall as a result of the crisis.

The CMA letter, written by its senior director, Howard Cartlidge, and obtained by the Private School Policy Reform thinktank, acknowledged that in the current crisis there may be a need for increased cooperation between businesses to ensure the supply of scarce products and services. This, however, did not give businesses a “free pass” to engage in non-essential collusion, he warned.

He told sector leaders: “We are sure that you share our concerns not just about the unacceptability of anti-competitive practices in the current circumstances, but also the risk of undermining public trust more widely across the independent school sector. It is therefore vital that any poor behaviour is nipped in the bud now.”

Robert Verkaik, a co-founder of Private School Policy Reform, said families who paid school fees would be dismayed by the revelation. “Those parents who have spent tens of thousands of pounds to send their children to an independent school will be rightly very angry if some of the schools are working against their interests by setting uncompetitive fees.”

It would not be the first time private schools have fallen foul of competition laws. In 2006 the Office of Fair Trading, which preceded the CMA, ruled that 50 fee-paying independent schools including Eton College, Harrow and Winchester had breached competition law by systematically exchanging information about pricing intentions. Each school was fined £10,000.

The CMA letter, dated 17 April, was also sent to other representative bodies in the sector, including the Headmasters’ and Headmistresses Conference, and the Independent Schools Association. They have been contacted for comment.

A CMA spokesperson said: “Where cooperation amongst businesses or other organisations is necessary to protect consumers in the coronavirus outbreak, the CMA will not take enforcement action.

“But we will not tolerate organisations agreeing prices or exchanging commercially sensitive information on future pricing or business strategies with their competitors, where this is not necessary to meet the needs of the current situation.

“We welcome the confirmation by the independent schools representative bodies to whom we have written that they are urging competition law compliance on their members.”

The ISC’s chief executive Julie Robinson responded: “We know of no evidence that schools are deliberately sharing information with each other and the CMA acknowledges that schools are striving to do the right thing.”