Britain has issued a last-ditch appeal to Greece to strike a deal with its creditors to prevent it being forced out of the euro with unpredictable consequences for the entire continent.
Chancellor George Osborne said the EU needed to be "prepared for the worst" after a meeting yesterday of eurozone group finance ministers failed to break the deadlock.
Hopes of preventing a disorderly "Grexit" by Athens from the single currency - with potentially far-reaching consequences for the rest of the EU - would now appear to rest with an emergency summit of the eurozone leaders in Brussels on Monday.
Greek prime minister Alexis Tsipras courted further controversy by staging talks in St Petersburg with Vladimir Putin, amid expectations he may ask the Russian president to throw him a financial lifeline.
Deputy Prime Minister Arkady Dvorkovich had said Russia would "consider" a loan to Greece, while Mr Putin's spokesman said: "We would do this because they are our partners and this is a normal practice between countries who are partners."
However, a Kremlin spokesman said the possibility of a loan "wasn't discussed", as the two leaders focused on "the necessity of developing investment co-operation".
The two countries' energy ministers had earlier signed a preliminary agreement on a pipeline to carry Russian gas to Europe via Turkey and Greece, bypassing Ukraine, in a deal which could be worth hundreds of millions of pounds a year to Athens after its completion in 2019.
With signs that Greeks are taking their money out of the banks in increasing amounts - with two billion euro (£1.4 billion) reportedly withdrawn in the last three days - Mr Osborne said the Treasury was stepping up measures to protect the UK economy from any fallout.
"We have entered the eleventh hour of this Greek crisis, and we urge the Greek government to do a deal before it is too late. We hope for the best, but we now must be prepared for the worst," he said as he arrived for a meeting of EU finance ministers in Luxembourg.
"In the United Kingdom we've taken the measures to increase our economic security so we can deal with risks like this from abroad. And clearly now we must go on and complete that plan."
Time is running out for the left-wing Syriza government which must find 1.6 billion euro (£1.15 billion) to repay the International Monetary Fund (IMF) by June 30.
Eurozone leaders are insisting they will only release the next tranche of bailout funds Athens needs to make the payment if it signs up to tough new austerity measures - something it is refusing to do.
Attending the St Petersburg International Economic Forum, Mr Tsipras sought to turn up the pressure on the Europeans, indicating that he could look to Russia for help instead.
Such a move would alarm EU leaders, threatening to undermine solidarity at a time when they are seeking to maintain pressure on the Kremlin over the continuing conflict in Ukraine, with the renewal of sanctions requiring unanimous approval from member states to prevent them expiring next month.
Standing alongside Mr Putin, the Greek prime minister said Russia was "one of the most important partners for us".
In an apparent nod to his hosts, Mr Tsipras said: "We are at the moment at the centre of a storm, of a whirlpool. But we live near the sea, so we are not scared of storms, we are not scared of open seas, and of going into new seas. We are ready to go to new seas in order to reach new, safe ports."
He called on the EU to return to its initial principles of "solidarity, justice and social justice" warning that "strict economic measures will lead us nowhere".
"The so-called problem of Greece is not just a Greek problem, it is the problem of the whole European Union," he said.
"We can't continue carrying the burdens of the past. If we continue doing so, continue making the same mistakes again and again, then we are doomed to failure."