David Hart, the union's general secretary, was due yesterday to recommend to his national executive that allegations made against the chief inspector by his former wife be set out in a letter to the DPP, as the Government has not yet launched a thorough investigation.
Mr Hart said: "I believe it is in the public interest to have a proper inquiry.
"The intention is to invite the DPP - in view of the evidence available - to instruct the relevant police force to investigate fully."
In fact, the DPP does not have the power to order the police to carry out a criminal investigation.
Mr Hart said the DPP could invite the police to investigate whether Mr Woodhead and his former pupil, Amanda Johnston, lied about the timing of their affair in sworn affidavits.
Although much discussed, the content of any affidavit remains a matter of speculation. Neither Mr Blunkett nor the national newspapers have seen the documents, said to be lodged with Mr Woodhead's solicitors.
Cathy Woodhead, the chief inspector's former wife, insists that her ex-husband lied when he claimed the affair did not begin until after Ms Johnston had left Gordano comprehensive school in Bristol.
However, Mr Blunkett said last week that the legal papers submitted to him by Mrs Woodhead contained nothing to substantiate the allegations made against her ex-husband.
Further pressure on Mr Woodhead to resign has come from senior Labour back-bencher, Derek Foster, joint chairman of the Commons select committee on education. Sixteen MPs have also signed an early-day motion demanding Mr Woodhead's resignation.