Parents of pupils attending a chain of three academies championed by education secretary Michael Gove and founded by his former schools commissioner have been told not to talk to the media about a £2m fraud to which it has allegedly fallen victim.

In a letter to parents written last month, Adrian Percival, CEO of Haberdashers' Aske's Federation Trust, which is based in south-east London and is responsible for 4,500 pupils, said: "The appalling crime appears to have been committed over a period of seven years, during which time the perpetrator appears to have set up a large number of small fraudulent transactions in order to commit these crimes unnoticed."

A 55-year-old man from Lambeth has been arrested in connection with the investigation, the Met police confirmed.

Percival wrote: "Given the ongoing nature of the criminal investigation, it is very important that nobody comments publicly on this situation, because this might jeopardise the success of any criminal trial that may take place. If you receive any inquiries from the media, I should be most grateful if you could refer them to me without offering any comment and we will deal with them appropriately."

The letter has angered some parents, who say rumours about the fraud have been circling for 18 months, during which time the federation failed to put them in the picture.

Percival, however, explained to parents in his letter that the issue had been disclosed in the federation's accounts, filed in March 2013. They state that, for the year ending August 2012, £1,047,788 had been lost through "unauthorised transfers" in 2011 and £924,316 in 2012.

The Haberdashers' Aske's Federation, which runs Hatcham College in New Cross, Knights Academy in Bromley and the Crayford Academy in Crayford, as well as a free school in Lewisham, was founded by Dr Elizabeth Sidwell, a teacher, whom Gove appointed schools commissioner three years ago, a position she held until recently. Sidwell continues to be senior education adviser to the government's University Technology Colleges Trust. According to a government website she "was appointed as schools commissioner by the secretary of state for education, and took post in May 2011. Her mission is to raise standards, tackle underperformance and champion the growth of academies, academy sponsors and free schools."

The federation is one of Gove's favourite academy chains. He has frequently cited it as a blueprint for other schools and visited it to make speeches, including one at Hatcham that went viral on YouTube as bored pupils struggled to stay awake.

The federation is believed to have been in the running to open another school in East Dulwich but a rival academy chain recently emerged as the front-runner.

The alleged fraud, which comes after Haberdashers' Knights Academy was judged by Ofsted in November to have "serious weaknesses", is likely to raise questions about the freedom given to academies. Critics complain that they lack financial oversight and are not accountable. Supporters say they give headteachers greater control over their curriculums and admissions.

The trust confirmed in its letter to parents that the Department for Education and the Education Funding Agency had been informed about the alleged fraud. It said it was trying to recover the lost money through the civil courts by seizing the offender's assets.