Speaking at a debate on electoral reform, hosted by The Independent, Mr Cook made an impassioned plea for a national consultation on the future of the voting system after the Government was elected with only 35 per cent of the vote.
The former cabinet minister said voters had a right to contribute to a review on how MPs are chosen and it was wrong to conduct the review behind closed doors.
Mr Cook called on the public to "demand ... that that review is opened up" and "made more transparent".
He said the review should "take evidence and meet in public" and "publish its reports so that the people who are involved in choosing the House of Commons are people who themselves have a say in this review and the way in which it [the Commons] is elected."
His demand for the Government to consult the people on PR was echoed by Simon Hughes, the President of the Liberal Democrats, who said the government must "honour" its manifesto commitment to carry out a review of the voting system.
Speaking at Making your Vote Count: the Way Forward, Mr Hughes said the electoral systems review, being conducted by officials in the Department for Constitutional Affairs, "must not remain a small exercise carried out by a few civil servants.
"After the civil servants and the ministers have deliberated, then Parliament and people must be invited to deliberate too," he said.
Following the review by the Department for Constitutional Affairs officials, it will be considered by a cabinet committee chaired by John Prescott, the Deputy Prime Minister, who has made clear his opposition for PR for Westminster.
But Mr Hughes said "the debate about fair votes for the House of Commons must also be seen as part of the debate about modernising all of the working of the British Parliament."
The debate held last night is part of The Independent's Campaign for Democracy which has now gained the support of 40,000 people or one in six Independent readers.
Simon Kelner, the Editor in Chief of The Independent, who chaired the debate, said the huge degree of public support for the campaign "gives the lie to the assertion that there isn't any appetite for voting reform."
Mr Cook paid tribute to The Independent's "magnificent" campaign on electoral reform. He said a House of Commons elected under PR would have not supported Tony Blair over the war in Iraq.
"If you had had a House of Commons elected by PR, you would never have had the war on Iraq in the first place," Mr Cook said.
Jean Lambert, the Green MEP, said proportional representation would give votes fresh value.
"It's important that you realise what electoral reform means to individuals. It's not surprising that people want to feel their vote has a value," she said.
Ms Lambert added that PR "doesn't necessarily end up with coalition government. If you do, so what?
"Because coalition government is good government."
Michael Brown, a former Conservative MP and an Independent columnist, said it was now in the Tory party's self interest to support PR because they would not get re-elected without it.
"It will be impossible for them to return to office under the vagaries of the current system," he said.Reuse content