Unison, the public-sector union, opposes changes to local management of schools proposed last week, which will delegate services including curriculum advice, repairs and payroll as well as meals.
It is being backed by the two largest teachers' unions, the NUT and NASUWT.
Schools will be able to buy-back services from the authority, look elsewhere or provide for themselves. But Unison, which claims up to 200,000 dinner staff among its members, argues meals services could be scaled down to become unviable. "Delegation is unworkable and undesirable," said Keith Sonnet, its head of local government.
Cash-strapped schools would be tempted to find savings in the kitchen to pay for books and new nutritional standards would be impossible to monitor, he said.
All the unions question the extra bureaucratic load on heads at a time when red tape is supposed to be cut. John Bangs, the NUT's head of education, welcomed the principle of defining which core services should stay with councils, but said ministers had picked the wrong ones. "Heads need more time to be professional, not less,'' he said.
The NASUWT was even more critical. Its deputy general secretary, Eamonn O'Kane, said LMS had not proved to be a blessing and should be reined in, not rolled out. "We see no reason to extend delegation other than the political one to sweeten the pill for grant-maintained schools," he said.
But the Secondary Heads Association, with 1,000 GM members, is also unhappy. Bruce Douglas, its president, said the one thing GM schools wanted to keep and others wanted delegated was money for school improvement and staff training - yet this would largely stay with local authorities. Ministers had "levelled down not levelled up", he said.
The formula has been interpreted as giving every school GM status - but this was strongly denied by Education and Employment Secretary David Blunkett this week.
"It is a total misconception that the announcement replicates the GM sector," he said. "It does not replicate unfair funding, it does not replicate opting out of the planning process for places or lack of accountability."