Academy budgets should be overseen by local authorities following a series of financial abuses, say council leaders.
Cash earmarked for education in England is too often "disappearing into the back pockets of those in charge", says the Local Government Association.
Current scrutiny is ineffective, leaving the media and whistleblowers to uncover fraud, argues the LGA.
The government says academies and free schools are subject to greater scrutiny than council-run schools.
Council leaders are urging Education Secretary Justine Greening to restore local oversight of all school finances "providing democratic accountability so that parents and communities can be confident their children aren't missing out".
They say the Education Funding Agency, the official body responsible for the financial oversight of academies and free schools, lacks the capacity "to provide the level of scrutiny necessary to ensure value for money and catch out fraudsters".
The LGA highlighted two scandals this year at:
In April, a report by MPs on the Public Accounts Committee raised concerns that the rapid expansion of the academies programme in England had made it difficult to keep track of spending and land.
In May, the government abandoned controversial plans to force all England's schools to become academies.
The Department for Education says all academies operate under a strict system of oversight and accountability which is more robust than in council-run schools and ensures any issues are identified quickly.
"Unlike other schools, their accounts are scrutinised by an independent auditor and we have considerably more financial information about academies than we ever had for council-run schools," said a spokeswoman.
"The academy programme puts control of running schools in the hands of teachers and school leaders, the people who know best how to run their schools.
"They also allow us to tackle underperformance far more swiftly than in a council-run system where many schools have been allowed to fail for years."
Richard Watts, chairman of the LGA's children and young people board, said: "We are told that academies and free schools are subject to more financial scrutiny than council-maintained schools, yet we keep hearing that millions of pounds of taxpayers' money, which has been earmarked to make sure our children get a good education, is disappearing into the back pockets of those in charge.
"The National Audit Office has raised serious concerns about the ability of the DfE to effectively monitor academy trusts' spending, even before the planned expansion of the academy programme, and we don't believe it can possibly have effective oversight of spending in more than 20,000 schools," said Mr Watts, who is Labour leader of Islington Council in north London.
"Centralising control of schools isn't working, oversight needs to be devolved down to local councils," he added.