Escaping Hoddle's destiny
Mr Blunkett said the "unfortunate incident I does not prevent him from continuing to do his job effectively".
Mr Woodhead's remarks - delivered during a question-and-answer session at Exeter University - came as Parliament considers legislation which would make it a criminal offence for teachers to have sexual relationships with 16 and 17-year-old pupils.
John Dunford, general secretary of the Secondary Heads Association, was "appalled" by the comments. He added: "I think this is a bit of a Hoddle-ism, someone sounding off on a topic out of their remit."
The remarks prompted the Mirror to ask why Mr Woodhead should not suffer a similar fate to Glenn Hoddle whose "ill-considered remarks" cost him his job as England football coach. But most papers concluded the chief inspector's gaffe was not a firing offence.
The Sunday papers raked up the affair Mr Woodhead had had with a former pupil exposed by the News of the World in 1995. The woman involved, Amanda Johnston, issued a statement saying that the relationship was "one of equals and was in no way improper".