Mr Woodhead has told council education directors that he wants to investigate 12 LEAs a year despite only having funding to cover four or five. A report on the first inspection in Staffordshire is expected in October. Next on his list are Cornwall and Barking and Dagenham.
Local authority leaders, who have their own proposals for evaluating performance, fear the plans may be over-ambitious given Mr Woodhead's problems meeting primary inspection targets.
First estimates by education directors are that a dozen LEA inspections would cost at least Pounds 1m a year. There are no indications yet whether the Government is prepared to raise the budget for the Office for Standards in Education.
The idea of inspecting LEAs was first announced by the Prime Minister in his speech to grant-maintained schools in Birmingham last autumn. Last month's White Paper outlined plans, with legislation expected this autumn. Mr Woodhead is known to be sceptical about the quality of council advisory teams.
The Standing Conference of Chief Education Officers and the Society of Education Officers have met Mr Woodhead to discuss LEA inspections. Roy Pryke, chairman of the Standing Conference and Kent's education director, estimated they would triple the present amount of inspection time and cost at least Pounds 1m a year. He said it could take up to 12 years to inspect every council and proposed a self-review arrangement for councils, linked to OFSTED.
Mr Woodhead told the council officers that he would be looking for examples of good practice and targeting authorities where there are significant problems.
And Heather du Quesnay, education director of the London borough of Lambeth and president of the SEO, said: "He seemed less concerned about getting round all authorities than in using the early experience to promote rigorous thinking on how LEAs need to operate and I find that encouraging."