Mr Woodhead has been under pressure since his former wife said he had an affair with Amanda Johnston, one of his former sixth-form pupils, while they were both at Gordano School, near Bristol. He has consistently denied this, although he and Ms Johnston admit that one began later.
Downing Street, urged by teaching unions to intervene to establish the truth of the allegation, yesterday stood by Mr Woodhead, claiming that he "still carries the confidence of the Prime Minister".
But Alice Mahon, the Labour MP for Halifax, called for Mr Woodhead to resign if it was proved that he had indeed lied about the timing of his relationship with Ms Johnston. "He's got to say whether it's true or not. If it is true, he's got a different set of family values from most of us in the Labour Party or in the country," she said. "I think he should go. It sets a very bad example for our children."
Mr Woodhead's former wife, Cathy, has accused him of lying. She told a newspaper at the weekend that he had confessed the affair to her in 1976, while he was still a teacher at the school and Ms Johnston was a sixth-form pupil. "My silence has condoned his lying. I feel I have protected him long enough," Mrs Woodhead said.