Two claims of “financial irregularity” at academies and free schools are being made each month, the Observer can reveal. There have been 58 allegations in the last three years – seven of which were made in the first three months of the 2015-16 financial year. The Department for Education (DfE) has refused to name the schools involved.

Last week the government announced the launch of 18 new free schools, adding to the 252 already open, with 98 more in the pipeline. David Cameron has said he wants every school to become an academy, which, like free schools, are outside the supervision of local authorities and have autonomy over their budgets.

However, figures released by the DfE have led to calls for an urgent examination of accountability in the system. In 2012-13, the first financial year in which allegations of potential fraud were collated, there were 11 such claims to the government’s Education Funding Agency (EFA). In 2013-14, there were 21 claims, and in the following year there were 19. Between 1 April and 15 July this year, there were seven allegations. Of the 58 allegations in total over the three-year period, six related to free schools.

Labour MP Gareth Thomas, a former teacher who is standing to become Labour’s candidate in the London mayoral election, said the statistics were “deeply worrying” and called for a review of the system: “‘These figures reveal a disturbing lack of proper controls and underline the continuing concerns about the lack of accountability of free schools and academies. A tough audit regime is now overdue to ensure the taxpayer gets value for money and standards of these schools are raised.”

Research commissioned last year by MPs on the education select committee warned that a host of “questionable practices” were being signed off due to loopholes in academy regulation.

The research – carried out by the University of London’s Institute of Education – found that while regulation had improved since 2010, there were serious potential conflicts of interest.

One witness interviewed by the academics described an academy headteacher who had spent £50,000 on a one-day training course run by a friend. Another cited the chairman of a multi-academy trust who used his company to provide all legal services for the trust.

The report cited a number of articles in the Observer in which questionable practices were exposed, including at the Academies Enterprise Trust, which runs 80 schools and has been barred from taking on more because of concerns about over-expansion. It paid nearly £500,000 into the private business interests of its trustees and executives over three years for services ranging from project management to HR consultancy, although a spokesman at the time said it had followed all the correct procedures.

There are also a number of cases of alleged fraud currently going through the courts. The founder of one of the country’s first free schools, Kings Science Academy in Bradford, and two of its senior members of staff are set to go on trial next year.

The three, all of whom have pleaded not guilty, are alleged to have made a series of unauthorised and unlawful payments into the personal bank accounts of the former principal, Sajid Raza, and of Shabana Hussain, a former head of department, out of a grant provided to the school by the DfE.

A DfE spokesman said: “Academies operate under a strict system of oversight and accountability – more robust than in council-run schools — ensuring any issues are identified quickly and we can take swift action. The Education Funding Agency keeps a close eye on academy finances and is well-placed to intervene on the rare occasions it is needed. The vast majority of the 5,048 around the country are run to the high standards we expect and we have a team of regional schools commissioners that work with the best local headteachers to further oversee the performance of academy trusts.”