An independent watchdog has secured a Pounds 62,000 grant from the Joseph Rowntree Charitable Trust for research into the working methods of the Office for Standards in Education.
The grant has been issued as part of the trust's commitment to work which "strengthens democracy and upholds the rights of the citizen".
Selected teams have been invited to submit tenders for the work, which should be published by November next year.
Mr Woodhead has been told about the research. "I hope (Ofsted) will not oppose this or be difficult," said Bob Fisk, a spokesman for the self-styled Office for Standards in Inspection.
Ofstin describes itself as "a voluntary, informal and independent group concerned to promote debate on the role and future of inspection". It was set up last year after a conference highlighted concerns about inspections.
Criticisms voiced at that time included poor methodology, conflicting aims, high cost, damage to the morale of teachers and an inadequate appeals process.
Some criticisms - particularly a lack of feedback - were accepted by Mr Woodhead when he spoke at the Professional Association of Teachers' conference in July.
The Joseph Rowntree Charitable Trust - which is distinct from the Joseph Rowntree Foundation, which also funds research, and the political Joseph Rowntree Reform Trust - is concerned with the use of power and the democratic process. But trust secretary Steven Burkeman said the decision to fund the research did not necessarily mean that trustees shared OFSTIN's concerns.
An Ofsted spokesman said that inspectors were accountable: "We're a government department subject to all the rules and conditions for public work."