Eurosceptics and europhiles are both demanding major reform of the European Union, according to a new report.
Mr Cash says he wants a consensus on the way forward
The European Reform Forum heard evidence from leading figures on both sides including ex-Europe ministers Keith Vaz and Denis MacShane.
ERF Secretary Bill Cash said the only way to achieve the reforms they wanted was to renegotiate existing treaties.
He denied renegotiation would pave the way for UK withdrawal from the EU, as claimed by Prime Minister Tony Blair.
Mr Blair has repeatedly accused Mr Cash of wanting Britain out of the EU - a charge denied by the Conservative MP.
Mr Cash said the existing EU treaties - such as the stability and growth pact - were "not working" and had led to slow growth, high unemployment and over-regulation in eurozone countries.
He called for an end to the "taboo" surrounding renegotiation, which has prevented the two main parties in the UK from discussing the issue.
He said he and others who shared his views had been branded "swivel-eyed nutters" in the past, but the debate had become more open since the European Constitution was rejected earlier this year by France.
Nevertheless, he said it was important to keep discussions moving forward, particularly as Germany would be attempting to salvage the constitution in the new year.
He called on both sides to "get your head out of the sand and let's get down to the serious business of trying to hammer out how we can get a sense of agreement" on the UK's future relations with the EU.
He denied trying to "put words into the mouths" of pro-Europeans such as Mr MacShane and Mr Vaz, by suggesting the only logical conclusion of their demands for reform was renegotiation.
The European Reform Forum heard evidence from dozens of witnesses over a six-month period, under the chairmanship of Lord Waddington, including ex-Foreign Secretary Lord Owen, former Tory ministers John Redwood and David Heathcoat-Amory, liberal commentator Will Hutton and former European Commissioner Lord Dahrendorf.
Mr Vaz told the Forum: "Now is the time to chart a new course for the [European] Union".
But speaking in the Commons on Tuesday, Mr Vaz rejected Mr Cash's call to return powers to national Parliaments and make the UK an "associate" member of the EU.
Mr Cash said this was the only way to "address the real question of how to accommodate the proper aspirations of the enlarged European Union and of Turkey".
But Mr Vaz, who praised the work of the ERF, which he said allowed cross-party debate of the issues, said he did not want to see a "two class Europe".
Speaking on Tuesday after his announcement of a deal on the European budget, Mr Blair spoke of the need for EU reform.
He said the union was "like a house that had many different rooms, constructed in different eras by different designers".
"The result is a building, but not one that really quite meets the needs of the modern world," he added.