An article by Mr Woodhead, who works for the Daily Telegraph on a salary of around pound;100,000, intimated that teacher unions are gaining the upper hand with ministers. And he predicted a drop in standards if proposals by David Hargreaves, chief executive of the Qualifications and Curriculum Authority, to scale down external examinations bore fruit.
He said The TES's front page last week, "Power to the teachers in the exams revolution", made it clear that Mr Hargreaves's intention was to rely more on teachers' assessment.
"No Miss Morris," Woodhead wrote, "... If you want to deliver higher standards in education then... you must hold firm on external tests and indeed inspections."
He added: "The unions hate the fact that schools are now accountable to the communities they serve. They would like nothing better than for the number of tests to be reduced and for teachers to be able to mark the few that remain themselves."
His successor Mike Tomlinson was attacked for wanting more user-friendly Office for Standards in Education inspections. A consultation paper on the future of inspections is due at the end of the month.
Mr Woodhead asked: "Is the integrity of inspection going to be sacrificed on the altar of teachers' morale? Are inspectors going to be encouraged to sweep difficult issues under the carpet?... OFSTED might as well be abolished now."
He said a move towards school self-evaluation must be avoided and said the Education Secretary's reaction to any changes to the inspection service would be a test of her resolve.
Ms Morris refused to comment on the article.