"He was for me a personal friend," Mr Prescott told around 1,000 mourners at the service at London university's institute of education. "I will miss my friend and our education hero.
"Ted made a huge contribution to education in our country. Children in the future may not know it but they will owe him an unrepayable debt."
Hundreds more people had wanted to attend the memorial service, attended by three former education secretaries: Shirley Williams, David Blunkett and Estelle Morris. The audience at the service watched a video filmed for the occasion by Teachers' TV, which included tributes from Neil Kinnock, the former Labour leader, and Rory Bremner, TV satirist and comedian.
Lord Kinnock said that Professor Wragg had been teachers' "great crusader".
Mr Bremner, who had been helped by Professor Wragg to write sketches on education, described him as a "climate of fun" who never lost his sense of mischief. He also said New Labour had lost one of its most effective critics who would be missed particularly as the education white paper goes through.
Lord Kinnock, who has criticised the white paper, said: "It is difficult to think of a (greater) loss to education, its creativity, and its values than the death of Ted Wragg. That would be true at any time in the decades of his life. It is particularly true now."
Other speakers included Fred Jarvis, a former general secretary of the National Union of Teachers. He said politicians who described Professor Wragg as out of touch were the true "unteachables".
"For what Ted advocated and campaigned for was based not on fleeting visits to schools for photo opportunities or urban dinner table gossip but many years of rich experience at the chalkface."
Donations to The Ted Wragg Memorial Fund, to provide educational opportunities for disadvantaged young people in Sheffield, should be sent to: John Bigley, Howden House, 1 Union Street, Sheffield, S1 2SH