Pressure mounts on Woodhead to resign
Mr Woodhead said in an interview with BBC Radio 4's The World at One on Wednesday that he would not quit but admitted the allegations "certainly don't make it any easier for me to do my job. It would be stupid for me to pretend otherwise".
Alice Mahon, Labour MP for Halifax, said Mr Woodhead should go if he was proved to have lied about when his affair with student Amanda Johnston began.
Teaching unions urged the Government to investigate, and complained that Mr Woodhead is being treated differently from ordinary teachers who, faced with similar allegations, would be suspended while an investigation was carried out.
The Department for Education and Employment is refusing to say whether it will investigate. Officials said David Blunkett, the Education and Employment Secretary, had nothing to add to his earlier statement made after Chris Woodhead had explained comments that relationships between teachers and students would be "educative and experiential". Mr Blunkett then said that "despite what Chris Woodhead has acknowledged, I believe it does not prevent him from continuing to do his job effectively."
Mr Woodhead's ex-wife Cathy sparked the new resignation calls by claiming in the Mail on Sunday that he had confessed to his affair in April 1976 - while still a teacher at Gordano school, Portishead, where Ms Johnston was a pupil.
In November 1975, Mr Woodhead said he wanted to move out of the family home in Bristol, according to Cathy Woodhead's account in the newspaper. The couple instead agreed that she and their baby daughter Tammy would visit her sister in Australia. She says Mr Woodhead admitted to the affair on her return to the UK from Australia in April 1976.
Earlier this year, when Mr Woodhead made his comments about relationships between teachers and students, he and Ms Johnston issued statements saying their nine-year relationship began in late 1976 - when both had left Gordano.
The row is particularly sensitive, given the Government's plans to criminalise relationships between teachers and students, even where students are over the age of consent.
Peter Smith, general secretary of the Association of Teachers and Lecturers, said the key issue was whether Mr Woodhead had misled the public about when the affair started.
"If what his ex-wife is alleging is correct, then Chris Woodhead has to ask himself whether his moral authority as HMCI is or is not fatally compromised," he added.
Nigel de Gruchy, general secretary of the National Association of Schoolmasters Union of Women Teachers, said it did not comment on individual cases, and that the affair highlighted the illiberal nature of the Government's proposed law on teacher-pupil relationships.
But he added: "Teachers can see how they would be treated in similar circumstances - suspension pending investigation."