Stephen Byers, the school standards minister, said there was wide variation in the amount that councils spend on "service strategy and regulation" (SSR) - for example, the costs of education committee meetings and the chief education officer's salary.
Total spending under this heading is Pounds 142 million, and Mr Byers says more of this money should be going directly to schools.
The minister was, however, described as ill-informed and lacking in integrity by David Wilcox, deputy chair of the Local Government Association. He said only 4 per cent of LEA spending was on administration.
But while ministers are waving a stick, their officials are being more pragmatic. All authorities have received a letter on accounting practices which advises them to ensure the dry-cleaning bill for the mayor's robes does not end up in the SSR budgets.