The Department for Education says there have been "serious failings" in the financial management of a federation of academies in Lincolnshire.
An investigation by department officials heavily criticises the Priory Federation of Academies Trust.
Richard Gilliland, the organisation's chief executive, resigned on 30 March.
The trust said "mistakes and errors of judgement" had been made by two individuals.
The government says the matter has been referred to the police.
The auditors' report was into the financial management of the trust, which runs four schools in Lincolnshire - The Priory Academy LSST, The Priory Witham Academy, The Priory City of Lincoln Academy and The Priory Ruskin Academy.
The report found that the trust's former chief executive Richard Gilliland had used the federation's credit card to buy training for his son valued at £4,000, purchase personal goods and to pay fees for tax advice.
It also concluded he had converted and decorated part of a property owned by the trust with the aim of moving in with his wife and had established a private apartment at a French property owned by the federation.
Mr Gilliland's daughter was hired by the trust as consultant and paid £55,500 for a year's work, the report said.
She was also paid nearly £900 in expenses for a trip to Bali "to establish an itinerary for a diving holiday for boarders".
Mr Gilliland's son was also employed for a few months.
The report also concerns the trust's former finance director, Steve Davies, who retired in December 2011.
The report's summary said: "The financial management of the federation has not been of a standard necessary for an organisation of its current size.
"Regularity and transparency in the use of public funds has not been demonstrated."
In a statement, the Priory Federation's chairman, Terry Coffey, said: "We have had rigorous audits, external reviews and compliance visits every year since the formation of the federation in 2008 - a total of 85 in all from nearly 20 different organisations, including the DfE. No organisation had ever raised any issues with us before.
"However, the trust recognises that mistakes and errors of judgement have been made in the past by two senior individuals who, before they left our employment, failed to comply fully with our internal systems."
The federation said most of the criticism related to employees who no longer worked for it, but changes were being made and "a more robust framework" would be put in place.
"As the report makes clear, a sum of money has already been repaid to the trust. We are currently reviewing whether any additional legal steps are required," the statement said.
A spokesman for the Department for Education said: "The department's investigation into the Priory Federation revealed serious failings of key individuals in relation to financial management. The trust has accepted responsibility and the CEO has now left. The department has also referred this matter to the police.
"Unfortunately no system of financial audit can guarantee it will prevent all wrongdoing."
The case has been taken up by critics of the academy programme in England.
The general secretary of the National Union of Teachers Christine Blower said: "This is quite an extraordinary abuse of position and power and confirms the NUT's fears about where the lack of accountability in academies can lead".
The government spokesman added: "The financial accountability systems in place for academies are more rigorous than those for maintained schools.
"Unlike maintained schools, academies must have their accounts externally audited. But lessons can always be learned and we will consider whether we need to strengthen our systems at federation level."