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Nearly 40% of England’s 2,900 academy schools have made payments to organisations with family ties to their directors or trustees, Labour found.

The Education Funding Agency discovered at least 26 cases last year where directors failed to declare a family link or the service was not provided at cost price.

The revelation raises fresh questions about the Government’s plans to turn all state primary and secondary schools into academies by the end of the decade.

Information unearthed through a series of Parliamentary questions found that 1,083 academy trusts (37%) had made “related-party transactions” in the financial year ending August 31, 2014.

A “related-party transaction” is when a payment was made to a businesses or organisations in which a director or trustee has an interest, either directly or through a family member.

The majority of these will be legal if the director or trustee registers their interest.

But the Education Funding Agency found there were at least 26 cases last year of “irregular” payments. It did not name any of the academies involved.

Whitehall spending watchdog the National Audit Office warned recently that the rapid expansion of academies has made it difficult to keep track of their spending.

The NAO said: “The department’s policy of autonomy for academies brings with it significant risks if the financial capability of the department and academies are not strengthened.

“And the financial statements do not present a true and fair view and meet the accountability requirements of Parliament.

“This will become even more significant in the context of the planned expansion of the academy sector.”

Read more:Heartbroken headteacher who resigned over Tory academy plan blasts "immoral" move

Shadow Education Secretary Lucy Powell said: “The Department for Education is totally failing to have a handle on the finances of the thousands of schools that it is trying to run directly from Whitehall.

(Image: Dominic Salter)

“It is plain to everyone, except the Government, that the Tory plan to force all schools to become academies will only make this situation even worse.

“It is time that David Cameron U-turned on this top-down, costly reorganisation of our schools system, which nobody wants and schools don’t need, and instead ensure there is proper local oversight of all our schools, so that standards are raised and parents can be sure their child’s school is getting the best deal for its pupils.”

However, a Department for Education spokesman said: “Academies and free schools operate under a strict system of oversight and accountability – more robust than in council-run schools – and we have consistently demonstrated that where we find failure, we will act quickly and decisively.

“The number of irregular or improper transactions is very small and we are confident that the accountability system for the academies programme is robust and fit for purpose.”

The lack of financial control of academies comes as Education Secretary Nicky Morgan is under mounting pressure to ditch her plans to strip local councils of control of schools - even from within her own party.

Tory councillors, MPs and peers, including former Education Secretary Kenneth Baker, have all voiced doubts about the programme.

The County Councils Network, which represents 37 local authorities, said plans to turn all schools into academies could lead to a “poorer education system.”

Chairman of the network Paul Carter, who is also the Conservative leader of Kent County Council, said: “My concern is that the change will lead to a poorer education system operating across Kent, and more broadly England, because the value that local authorities generally provide to schools will be removed.”

He added: “If you have a school with five teachers, and two or three of those teachers become pregnant at the same time, you need those support networks to support those schools - otherwise their finances will not be sustainable and the school will end up in a spiral of decline.”