Members of the Commons Education and Employment Select Committee plan to cross-examine the Ofsted head about his remarks when he appears before them on Wednesday.
Mr Woodhead provoked outrage by saying that affairs between teachers and pupils could be "experiential". The row was fuelled yesterday when it was revealed that he had once been involved with a former pupil.
David Blunkett, the Education Secretary, and Jack Straw, the Home Secretary, are both said to be dismayed by his remarks. The Home Office is currently piloting a Bill which will make it a criminal offence, punishable by up to two years in jail, for a teacher to have sex with a 16- or 17-year- old pupil.
Ministers privately expressed concern about his comments although they were instructed not to say anything. Teachers' leaders called on him to resign. "I don't know what he thinks he is doing," one minister said. "There should never be a sexual element to the relationship between teachers and young people." Another
minister said: "He is not popular with a lot of people in Government and this will do nothing to improve that."
Mr Woodhead provoked the row by saying he did not believe teachers should necessarily be "drummed out of the profession" for having a relationship with a pupil over the age of 16. "I think human beings can get themselves into messes and I think those messes can sometimes be experiential and educative on both sides," he told student teachers at Exeter University. Yesterday he backtracked, saying the remarks were not his "true stance" on the subject but had been made to reassure an individual student.
Some critics raised the issue of his judgement by referring to his friendship with one of his former sixth-form pupils. Mr Woodhead met Amanda Johnson at Gordano School in Bristol, where he taught her literature. A relationship which began when he was no longer her teacher and after he had separated from his wife, continued for nine years.
Ms Johnson, now 41, backed her former lover's comments, saying, "I think what he said was fairly reasonable." Asked if their relationship had been "educative" she said: "We had a relationship, a good relationship. I don't know whether `educative' would be a term that would spring to mind."
She added that she felt Mr Woodhead was being hounded by his critics. "I heard that people are saying he had a relationship before I left school which is totally unfounded."
Officially, the Department for Education and Employment yesterday refused to discuss the remarks, but a friend of the Education Secretary said the row would be "embarrassing" to the Government.
David Hart, of the National Association of Head Teachers, said Mr Woodhead may have to resign. "Under no circumstances can anybody condone relationships between teachers and their students. They are dismissable offences and they could be criminal offences."Reuse content