David Cameron has issued an ultimatum to the Greek people that fresh elections must decide once and for all whether the country stays in the eurozone.
The Prime Minister insisted failure to provide clarity could prove disastrous for the world economy.
The message came as his Cabinet colleague Ken Clarke said the European banking system was already "in tatters".
Clarke warned that Britain was "heavily exposed" to potential problems and could be among the next targets for market speculation.
Deputy Prime Minister Nick Clegg also criticised the lack of leadership on the eurozone crisis, raising fears of a rise in extremism and civil unrest unless it was addressed.
Cameron, in America for back-to-back G8 and Nato summits, said talks with fellow world leaders had "crystallised" the problems.
"We now have to send a very clear message to (the Greek) people - There is a choice, you can either vote to stay in the euro with all the commitments you have made, or, if you vote another way, you are effectively voting to leave," he said.
"The crucial thing is that eurozone leaders have to put in place contingency plans for both of those eventualities - really clear plans to keep our economies safe and stable."
He went on: "What I think would be bad for Greece, bad for Europe, bad for the world would be if we just allowed the can to be kicked down the road with an inconclusive outcome," he said.
"It has just got to try and make sure that this is a moment of clarity and decisiveness for the eurozone."
The premier indicated that German chancellor Angela Merkel - who has driven the demands for austerity and fiscal discipline within the eurozone - had shown signs of a willingness to compromise.
"I think she did show some flexibility in terms of what more can be done on the growth agenda and also what more can be done to handle the risks inside the eurozone," he said.
"The fact that you have got countries like Japan, America, Canada round the table, as well as Britain, who are outside the eurozone but affected by what happens inside the eurozone, I think, was helpful in bringing that important pressure to bear."
Justice Secretary Mr Clarke, a former chancellor, said Greek voters had to "face up to reality".
"These are hardships inflicted on them by the irresponsibility of their former politicians," he said.
"But they cannot just vote for saying, 'could people just carry on giving us some money so we do not have to change anything'."
Clarke said the consequences would be "serious" if the Greek people elected "cranky extremists" and defaulted on their debts as a result.
"No-one knows exactly what will happen in the rest of Europe. But the banking system is in tatters, it is weak in very many places," he went on.
"We don't know what the knock on effects would be, they could be very serious and of course people will start barking at the door of Portugal, Ireland, Italy and here in Britain.
"Our banks are heavily exposed to some of these countries, we have recapitalised them so far... I obviously hope the Greeks will vote responsibly and that we can avoid turmoil."
Meanwhile, Clegg warned that Germany must do more than merely insist on austerity if the eurozone was to stabilise.
He also admitted that the coalition may have been too "dogmatic" in its rhetoric on cutting spending.
In an interview with Der Spiegel ahead of a visit to Berlin this week, the Liberal Democrat leader said: "You have to have something which creates a fiscal accompaniment to monetary union.
"Whilst I have a huge amount of sympathy with German taxpayers and German politicians who are reluctant, understandably because Germany is the paymaster of the European Union, to entertain these ideas, I fear that they are unavoidable.
"It is not sustainable to believe that the eurozone can thrive through fiscal discipline alone - it also has to, at some level, include an ability to either share debt or to deal with shocks in one part of the system or the other through fiscal transfers."
Clegg hit out at a lack of leadership on the eurozone crisis, cautioning that there could be a rise in extremism unless it was addressed.
"This cannot carry on, because the combination of economic insecurity and political paralysis, we know this from the history of our continent, is the ideal recipe for an increase in extremism and xenophobia," he said.
Clegg denied that the coalition parties were "austerity fanatics".
"Maybe our rhetoric has been too dogmatic in the early stages because we needed to persuade people it was necessary," he said.
Clegg insisted people should look at what the government had "actually done".
"Last autumn when I was told, when David Cameron was told, when George Osborne was told that the predictions of growth and the public finances in Britain were worse than we'd anticipated what we could have done was to cut more to meet our initial target in dealing with the structural deficit by the end of this parliament," he said.
Shadow chancellor Ed Balls told Murnaghan that it would cause "huge damage" if Greece made a disorderly exit from the eurozone.
"Greece needs to stay in for at least as long as the eurozone needs to sort its act out," he said. "And I am afraid that is taking a very, very long time."
Labour leader Ed Miliband said he had coined a new phrase - "Cam-Mer-Kozy economics" - to sum up the approach taken by the Prime Minister, German Chancellor Angela Merkel and former French president Nicolas Sarkozy over the last two years to tackling the eurozone crisis.
He added: "It's about collective austerity and it hasn't worked.
"It is time to wake up and recognise it and that's what the Prime Minister needs to do.
"Over the last few days he has found himself beached somewhere between President Obama and President Hollande and Chancellor Merkel, not quite sure where he is."
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