The former TES columnist exercised a quiet influence throughout Baroness Morris' five years at the Department for Education and Skills.
She said: "He was a good friend and loyal counsellor during all the time that I held ministerial office. If his Sunday evening phone call started, "How do you think it went?", you knew you'd got it wrong. He contacted me weekly with 10 or more ideas about what I should do."
Baroness Morris was speaking at the first of two memorial services held in memory of Professor Wragg, who died of a heart attack last November.
The service, at Exeter cathedral last Saturday, was attended by more than 700 people. Speakers included Steve Smith, vice-chancellor of Exeter university.
Professor Wragg's nine-year-old grandson, Harry Williams, described how his grandfather taught him to ride a bicycle, despite being unable to ride himself. "People say I am like my granddad, and I loved him," he said.
A second memorial service will be held on February 15, at the Institute of Education, in London. More than 1,000 people are expected to attend the service, which is sponsored by The TES, The Guardian, the Institute of Education, the Teaching Awards Trust, Teachers' TV, the British Educational Research Association and the New Vision Group.
The event will launch The Ted Wragg memorial fund, which will provide educational opportunities for disadvantaged young people in Professor Wragg's home town of Sheffield.
Judith Judd, TES editor, said: "We are very pleased to support this celebration of the life of Ted Wragg, whose brilliantly satirical TES column cheered up teachers for more than 25 years. We hope that our readers will want to contribute to the fund in his memory."
Donations to the Ted Wragg fund should be sent to: John Bigley, Howden House, 1 Union Street, Sheffield, S1 2SH.