The blackballing has been confirmed by a minister involved at the time and is revealed in a supplement published in today's paper in tribute to Professor Wragg, who died in November.
When Labour won power in 1997 Mr Blunkett wanted Professor Wragg to sit on at least one of the taskforces set up to help implement the new Government's education policies.
The pair knew each other well and shared a working-class Sheffield upbringing. 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 always rejected his name.
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."
A Downing Street spokesman said: "We do not recognise these reports."
Professor Wragg became a trenchant critic of Labour education policy, using his TES columns to lampoon what he regarded as the malign influence of "Tony Zoffis".
But the rejection did not prevent him acting as a sounding board for several Labour cabinet ministers. As well as regular chats with Mr Blunkett and John Prescott, the Deputy Prime Minister, 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 Professor Wragg ennobled, but his family say he was phlegmatic about never being offered an honour.
"Dad's only political party was education," said his daughter, Josie. "If he had written a particularly biting article he used to joke 'There goes another knighthood'."
A memorial service is being held at Exeter cathedral at 11am tomorrow and a tribute will be screened on Teachers' TV at 9.30pm.