The Chief Inspector of Schools said he was ruling out legal action as it "would not be in his interests".
Mr Woodhead has denied claims made by his ex-wife in a Sunday newspaper that he had an affair with Amanda Johnston while she was a pupil at Gordano school near Bristol.
Mr Woodhead has always maintained that the relationship did not start until they had both left the school. Ms Johnston has backed his version of events, saying there was nothing improper about their relationship while they were at the school.
He told BBC Radio Four's The World at One yesterday that he would not resign. But he admitted the controversy made his professional life more difficult.
The allegations "certainly don't make it any easier for me to do my job. It would be stupid of me to pretend otherwise." But, he said, "there's a vitally important job to do and I shall continue to do it to the best of my ability".
He ruled out going through the courts as it would not "be in my interests or, more importantly, the interests of thosenearest and dearest to me".
Mr Woodhead was at the centre of a storm of protest last month when The Independent revealed he had told an audience of student teachers that relationships between teachers and pupils could be "experiential and educative". Downing Street made clear on Monday that Mr Woodhead "still carries the confidence of the Prime Minister". But yesterday head teachers said they were "disappointed" that Tony Blair had not instigated an inquiry into the claims.
John Dunford, general secretary of the Secondary Heads Association, said: "I do think the Prime Minister owes it to the education system to look into this. We want a school inspection system which has the broadest respect, not only among teachers but among the general public. We need to get to the bottom of things like this to preserve the reputation of the system."
David Hart, general secretary of the National Association of Head Teachers, said it was important to establish which version of events was true. "Clearly the Government wants him to stay. If [not] they would carry out an inquiry. I don't think the Government wants to know what the real position is," he said. "The Government really cannot have this both ways. It's in the middle of pushing a Bill through Parliament which states it is a criminal offence to have a relationship with a pupil whilst that pupil is at school."
Under the Sexual Offences (Amendment) Bill, currently passing through the Commons, teachers face up to two years' jail if they have sex or "any sexual activity" with pupils aged under 18 at their school.Reuse content