Boris Johnson upped the pressure on David Cameron by demanding he negotiate a far looser relationship with Europe - and hold a referendum on the new deal.
The London Mayor said Britain should exploit the eurozone crisis to free itself from key areas of the European Union (EU), including fisheries policy, social policy and farming subsidies.
Johnson also risked angering Downing Street by pre-empting a long-awaited speech by the Prime Minister on the issue and criticising his support for closer eurozone integration.
The intervention came amid growing tensions in the Conservative Party over the traditionally thorny issue of Europe.
Cameron has hinted that he is ready to promise a referendum over UK membership but is facing growing calls to clarify his position.
In a speech on Monday, former Cabinet minister and leading right-winger Liam Fox will warn that the party must have a "clear and concise" policy in place by next autumn.
Speaking on Sky News' Murnaghan programme on Sunday morning, Johnson rebuffed suggestions from some Tory backbenchers for an immediate national vote on membership.
But he endorsed Fox's timetable and said Britain should strip back its participation in Europe to the single market.
"If we have a simple in-out referendum, I think at the moment the chances are that the British people would say, stuff that for a game of soldiers - 56% say let's come out," the mayor said.
"The really good bit about it (the EU) is the single market. That is something that allows British enterprise to trade freely with other European countries in a way that I think might be imperilled if we were to come out unilaterally.
"So, what I am saying is let's have a renegotiation in which we chop off all the kind of bits we do not like. Chop off all the excrescences like the fisheries policy, and the social chapter... why on earth are we continuing with that (Common Agricultural Policy) in this day and age - it is grossly unfair.
"That renegotiation is essential, because at the moment our European friends and partners are continuing to make this disastrous mistake.
"They are compounding the mistakes of the euro by going forward full tilt with political and fiscal union, which, by the way, this Government, our Government, should be opposing."
Johnson predicted that Cameron would commit to a referendum in a long-awaited keynote speech on the issue - expected before or just after Christmas.
"I reckon he's going to commit to a referendum, which will be broadly an in-out referendum on the new terms," he said.
"We have got to go on and get a better deal for Britain, which is basically the single market, making sure that British ministers are in the internal market, able to protect British interests, making sure that British companies continue to have unfettered access to that market and the reciprocity, but allowing the others to go ahead with this fiscal union in which frankly we do not want to participate and should not participate.
"But I think the new deal, us allowing them to go ahead, should be our price for the new arrangement.
"We should say to them, 'look the euro was not a good idea, it is proving to be a disaster... if you want to go ahead with this crack-brained project to create a single country out of 17-20 totally different countries, OK, you won't have our approval, but you will have our permission.
"In exchange we want a new relationship. We want the single market'.
"That's a deal I think we should put to the British people."