And this new lack of accountability could discourage potential donors, it is feared.
The School Standards and Framework Act, which became law last month, provides for the new categories of foundation (grant-maintained) and voluntary (church) schools to be exempt charities.
Exempt charities are not subject to the usual regulatory framework managed by the Charities Commission and applicable to community (local education authority) schools. The Funding Agency for School says exempt charities are instead usually held accountable to some other regulatory body, such as education authorities.
However, the FAS says its abolition next year will leave grant-maintained schools' charitable funds unsupervised.
Combined with similar funds held by church schools, the sums involved could add up to pound;1 billion - covering everything from fund-raising for a new school minibus to donations for new buildings.
"Without effective regulation arrangements the donors of these funds may be more reluctant to make donations to schools, thereby reducing the total amount of funds available to schools and increasing pressures on the public purse," says the agency, in its response to the Government's Fair Funding document on delegation to schools.
"The lack of accountability of these funds would also be contrary to recent initiatives to make charities more accountable. It is also clearly inconsistent with the principles governing the new approach to schools, in particular those of accountability, transparency of funding and equity for all schools."
"Non-public income" accounted for nearly 9 per cent of GM schools' annual income in 1996-97, and is expected to rise further.
David Lankshear, the Church of England's schools officer, welcomed the Act because it clarifies the charitable status of church schools. However, the CofE plans to issue guidance to schools on managing their charitable accounts next term.
He suggested that education authorities should step into the vacuum left by the departure of the FAS in respect of foundation schools.
"We are concerned that all money raised for schools is properly accounted for and properly used. We want good practice," he said.
"The issue will be for foundation schools that don't have a religious identity. Their supervision will have to come either from the Charity Commission or local authorities, using guidance similar to that we have developed."
However, a spokesman for the FAS said neither local authorities nor the Charity Commission have the powers to examine the accounts of exempt charities -which was why the agency was drawing the issue to the Government's attention.
A spokeswoman for the Department for Education and Employment said that it had received 3,000 responses to the consultations on Fair Funding, and was unable to comment on individual submissions.
"We can confirm that the Fair Funding framework will include requirements as to financial reporting and audit," she added.