Mr Woodhead has recently announced that British schools should use whole-class methods in at least half of all teaching and in 60 per cent of maths lessons.
But Professor Robin Alexander, formerly one of the Government's "Three Wise Men" advisers on primary education - along with Mr Woodhead - this week accused the chief inspector of using whole-class teaching as an "off-the-peg" solution. He said that Mr Woodhead has become a victim of his own "dogma".
Although himself a critic of much primary teaching, Professor Alexander defended British schools and described the chief inspector's evidence as "extremely limited".
He also attacked the "bizarre consensus" between Labour and the Conservatives, accusing both parties of political opportunism. "The political right and left jockey for territory hitherto held uncontested by the Right," he told the audience at the University of Warwick's annual Blythe Lecture.
"The claim of politicians that there is a new consensus about primary education is really no more than an acknowledgement that it is politically expedient in the short term for government and opposition to sing the same tune."
Professor Alexander acknowledged that Britain is underachieving economically and educationally. But, he said, "history teaches that off-the-peg borrowing of educational practices of the kind that is currently being commended for primary schools may not work.
"History also teaches us that primary education in England has for too long been driven by the arbitrary swings of the pendulum of fashion. In this it is unfortunate that a chief inspector who since 1992 has criticised the 'dogmas' of primary education should now appear, alas, to be hooked on his own."
Professor Alexander said that "whole-class teaching" is, without further definition, too vague a concept. "It covers a very wide variety of practices, takes many different forms and serves many different purposes.
"What do India, Bangladesh, Zaire, Malawi and Vietnam have in common? They are all low-income, low GDP and low GNP economies. They have some of the world's lowest secondary and higher education graduation rates. And what else? They all use whole-class teaching as the main method in their primary schools."
He said that the international research used by Mr Woodhead to conclude that Britain needs more whole-class teaching has crucial weaknesses.
Data from the International School Effectiveness Research Project, he said, used evidence from just 12 of the 25,000 primary schools spread over the UK, and only 12 of the 80,000 elementary schools in the United States.
"The scope in this study for accessing empirically the peculiarly English brand of 'progressive' primary practice which has been fingered as the principal culprit in this country's educational failure was, to say the least, extremely limited."
In particular, he criticised the "conceptually untenable" failure to see cultural factors as intertwined with teaching methods. "Life in schools and classrooms is an aspect of our wider society, not separate from it: a culture does not stop at the school gates.
"The strengths of our primary schools are the strengths of our society; their weaknesses are our society's; their tensions mirror and illustrate the fractured and unstable nature of British culture in the late 20th century. "
Teaching methods in France, for example, could not be divorced from the French people's love of conversation in their own language: an enjoyment that was not so conspicuous among the British, he said.