The blackballing has been confirmed by a minister involved at the time and is revealed in a TES supplement published today in tribute to Professor Wragg, who died in November.
The outspoken education academic knew Mr Blunkett well. They shared a working-class Sheffield upbringing and a commitment to improving educational standards. It is understood that when Labour won power in 1997, Mr Blunkett wanted Professor Wragg to sit on at least one of three taskforces set up to help implement the new Government's education policies.
The standards taskforce famously included Tim Brighouse, then Birmingham chief education officer and Professor Wragg's friend and ally, alongside their professional nemesis Chris Woodhead, then chief inspector of schools in England.
At the time, Professor Wragg welcomed the resumption of a healthy tradition of ministers taking advice from education professionals. But it is understood that there was no place for the director of Exeter university's school of education because the Prime Minister's office rejected his name.
A Downing Street spokesman said: "We do not recognise these reports." Mr Blunkett's office said he did not wish to comment.
But in a tribute, the former education secretary said: "Ted Wragg was not simply an outstanding academic but a great communicator who could turn theory into practical, political change."
Professor Wragg became a trenchant critic of Labour education policy, lampooning what he regarded as the damaging influence of "Tony Zoffis". But the rejection did not prevent him acting as a sounding board. He was one of the last people Estelle Morris spoke to before she resigned as education secretary in 2002.
Senior politicians were keen to see him enobled, The TES understands, but his daughter Josie said: "Dad's only political party was education. If he had written a particularly biting article he used to joke, 'There goes another knighthood'."
More than 900 mourners are expected at a memorial service at London University Institute of Education on February 15. Tomorrow will see a memorial service in Exeter Cathedral at 11am and a tribute will be screened on Teachers TV at 9.30pm.