The news leaked out on Tuesday that the Office for Standards in Education intends to adjust the way inspectors grade teachers' performance in confidential reports to heads. Mr Woodhead was asked on the BBC Today programme whether "you regard a test of the success of this policy that more teachers are sacked?"
"Yes," he replied. "If teachers are not doing the job they are paid to do they should not be in post." He went on to accuse OFSTED inspectors of being too soft.
This predictably raised union hackles and heightened the suspicion that the change had been introduced in order to make it easier for larger numbers of teachers to be labelled unsatisfactory, making it easier to get rid of them.
Inspectors are already obliged to inform heads if any of their teachers are either at the top or the bottom of a seven-point scale.
But last year, it emerged that out of 2,862 inspections, only 88 teachers had been given the bottom two grades - casting doubt on the chief inspector's famous assertion that there are 15,000 bad teachers.
Mr Woodhead blamed his own inspectors, suggesting that they had become infected with educational orthodoxy and were too reluctant to hand out the lowest grades.
From September, inspectors will still grade lessons from one to seven, but reports on individual teachers will put the seven grades into three groups: excellentvery good, goodsatisfactory, and unsatisfac torypoorvery poor.
This, said an OFSTED spokesman, will make it more difficult for inspectors to pull their punches: "The previous code required some fairly uncomfortable confrontations between inspectors and teachers; there was a temptation for inspectors to fudge the issue and nudge grades up from six (poor) to five (unsatisfactory, but not bad enough to be worth reporting). But to change a grading from unsatisfactory (three) to satisfactory (two), the inspectors would really have to wrestle with their conscience - it's a much bigger difference."
OFSTED insists that the new system is not intended to be used as the basis for disciplinary action, and admits that heads would not have grounds to use the evidence from the confidential reports in disciplinary proceedings. It is intended merely to provide extra information for heads and more feedback for teachers, said the spokesman. He also said that it was "unlikely" that teachers would in future get a formal interview with the inspector in order to discuss the way they had been marked.
While it is difficult to see that the change will make sackings easier (inspections only take place every six years and there can be few heads who need to wait for OFSTED to tell them if they have inadequate members of staff), it could mean that there will be a jump in the number of teachers labelled bad.
The Government is consulting local authorities and unions about speeding up the process of removing incompetent teachers, probably by looking at their performance against the annual targets that each school now has to set, but as yet there is no indication of how any change would fit with existing employment law.
The grading change is part of a package of "refinements" of the inspection system to be announced next week. Doug McAvoy, general secretary of the National Union of Teachers, has written to the Education Secretary asking why the proposed changes were not included in last week's White Paper.
But Ofsted has been talking to the teacher unions about the proposals, and argues that the change to the grading system is merely a response to what heads want.
David Hart, general secretary of the National Association of Head Teachers, admitted that he had originally had no objection to the change in the grading system, but told the TES that the way the chief inspector presented it was "unfortunate " and likely to provoke paranoia in the profession.
"We had responded positively to the proposals, but now people are bound to be suspicious of the motive behind the change - that the chief inspector is trying to force the inspectorate to put more staff into the poor category so as to justify his assertion about 15,000 incompetent teachers," he said.
Peter Smith, general secretary of the Association of Teachers and Lecturers, said that the real problem was that inspectors knew that they could not make sensible judgments about a teacher's calibre on the basis of a snapshot. "OFSTED is trying to play its part in the crusade for standards by trying to do something it is not possible for OFSTED to do."
Nigel de Gruchy, general secretary of the National Association of Schoolmasters Union of Women Teachers, said the new system was crude: "Teachers will suspect that with all the Government's talk about 'zero tolerance of failure', it will be a simple question of 'three threes and you're out'."
In Croydon, London, an attempt to speed up the removal of incompetence staff by giving an "improve or go" ultimatum to nine teachers at the Ingram high school has met with threats of industrial action from the NUT.