Environment Secretary John Gummer is accused of illegally handing Pounds 77,000 over to the Further Education Development Agency.
Local authorities are angry that they have lost the cash and are challenging Mr Gummer to hand it back.
The decision to take the cash has sparked a new row over conflicts of interest between LEAs and colleges and led to renewed calls for a forum to represent all parties involved in the planning of education and training post-16.
LEAs were initially allocated the cash to fund one of FEDA's predecessors - the Staff College, and they were represented on the college's board.
Later when the then Education Secretary John Patten refused to allow LEAs representation on the new FEDA board local authorities withdrew their support and demanded the cash back.
Graham Lane, chairman of the Council of Local Education Authorities, said Mr Gummer took the money without proper consultation after he was told that the LEAs were not willing to support the agency.
Mr Lane, said: "What Mr Gummer has done is demand taxation without representation.
"We called for the cash to be diverted to the National Institute for Adult Continuing Education since local authorities still have an interest in lifetime learning."
In a letter to Mr Gummer last week, he asked: "Will you please arrange for these illegal payments to be stopped and for the grant to be switched to the NIACE at the earliest possible opportunity?" A Department of the Environment spokesman insisted that Mr Gummer was acting on legal advice that the money was already committed to FEDA. Mr Lane insists, however, that they have had legal advice to the contrary.
Stephen Crowne, chief executive of FEDA, appealed to LEAs not to abandon the agency. "Irrespective of the outcome of the funding row we are committed to working very closely with LEAs and supporting adult and continuing education. "
Meanwhile, Labour has pledged to eradicate scope for such anomalies if it comes to power. Bryan Davies, Labour's further and higher education spokesman, has spelt out in stronger terms than ever his party's commitment to regional councils which would take over some of the funding and policy powers from central Government and its national agencies.
Regional councils would have members from colleges, LEAs, employers and training and enterprise councils. They are likely to be shaped around the nine FE regional committees.
Mr Davies said the latest grant fiasco was typical of inefficient management by the Government which marginalised local authorities whatever the costs.
"We are looking at ways of strengthening the regional structures, to remove the confusion of different uncoordinated actions by Government departments and to help both LEAs and colleges run more efficiently."
He stressed that this did not mean abolition of the Further Education Funding Council, which would have a national co-ordinating role under a new Labour government.
But his pledge to devolve powers will not be liked by Sir William Stubbs, FEFC chief executive, who insists that regional tiers of government must be resisted.