He has told councils to concentrate on "incompetent teachers" and, in a separate memo passed to The TES, he has told his staff that council advisers and inspectors need tougher scrutiny. He has also ordered an investigation into how this might be done.
"I am increasingly convinced that we should focus on whether LEAs are using their resources efficiently in order to support schools in raising standards of pupil achievement," he said.
In the official minutes of a recent meeting with leaders from the Association of Metropolitan Authorities, Mr Woodhead says that some LEA teams have built up "a culture of dependency" in order to sell services. "Inspection and advisory services established as business units had a financial interest in surviving, " he says, "and often would not tackle difficult issues in their dealings with schools."
These remarks follow his earlier criticisms of Office for Standards in Education inspectors who tout for private advisory business while conducting OFSTED inspections.
He suggests to the councils that they should spend less time with good schools and more time on "incompetent teachers" and schools with "serious weaknesses".
Explaining the comments further, a spokesman for the OFSTED said, "Many LEA teams have to make a certain amount of money. In order not to lose the interest of schools it may be that some will tend to say nice things rather than being particularly frank."
An immediate shake-up of LEA advisory teams, as requested by the Prime Minister in a speech to grant-maintained heads in Birmingham, was not likely, he said, as implementing the four-year inspection cycle is a priority.
Local authorities were compelled to put their advisory services on a semi-independent "agency" footing when the OFSTED was created in 1992.