Greece and its eurozone partners must get involved in discussions to find a "sustainable solution" to the country's debt crisis, Downing Street has said.

Prime Minister David Cameron held emergency talks with Bank of England Governor Mark Carney and ministers including Chancellor George Osborne to discuss the possible impact on the UK of Sunday's referendum in Greece, which delivered a landslide 61%-39% No vote to austerity measures demanded by creditors in return for a new bailout package.

Greek finance minister Yanis Varoufakis has quit to smooth the path for further negotiations, while the two biggest players in the eurozone - German chancellor Angela Merkel and French president Francois Hollande - were meeting in Paris for crisis talks ahead of a summit of single currency leaders in Brussels on Tuesday.

Following this morning's meeting in Whitehall, Mr Cameron's official spokeswoman told reporters: "The Prime Minister's view is that this is an issue that needs to be discussed between Greece and its eurozone partners. It is for them to work together on a sustainable solution."

The spokeswoman declined to say whether Mr Cameron thought that the solution should involve Greece leaving the single currency.

Asked whether the PM wanted the country to remain in the EU, she replied: "We supported Greece becoming a member and we support the EU at 28 (member countries)."

Mr Osborne was due to update MPs on the situation in Greece in a statement to the House of Commons at around 3.30pm. Meanwhile, the Foreign Office's travel advice has been updated to reflect the outcome of Sunday's poll.

British tourists are advised to make sure they take "sufficient euros in cash to cover the duration of your stay, emergencies, unforeseen circumstances and any unexpected delays" as well as to take security precautions against theft.

The advice adds: "There are currently no restrictions on taking unspent euros out of Greece at the end of your stay."

The Foreign Office did not advise against travel to Greece, but warned: "Visitors to Greece should be aware of the possibility that banking services - including credit card processing and servicing of ATMs - throughout Greece could potentially become limited at short notice."

Mr Cameron spoke briefly by phone with Dutch PM Mark Rutte as results came in on Sunday evening, and may speak to other EU leaders over the coming hours and days, said his spokeswoman.

She made clear that the PM believes the priority is for eurozone countries to discuss the crisis with Greece, but added that if issues emerged which affect the EU as a whole, it may be necessary later for all 28 leaders to meet.

Although Britain's direct exposure to Greece is limited, Downing Street warned that the UK will not be "immune" to any fallout from the crisis. Today's meeting received an update on contingency plans put in place over recent months to deal with possible impacts on British banks, businesses and holiday-makers, as well as the 40,000 British residents in Greece.

Mr Cameron's spokeswoman said: "The PM is clear that it is in the interests of the UK that we are outside the eurozone and therefore have one of the fastest-growing economies in the world at the moment. We should keep taking measures to support that, while recognising that we are not immune from what happens in the eurozone and we have got to keep taking the tough decisions needed to make sure our economy continues to grow."

Greece's future in the EU is hanging in the balance with warnings that a new bailout deal is needed swiftly to avoid a catastrophic financial crash that could send it spinning out of the single currency.

The result of the referendum represented a sensational victory for radical left premier Alexis Tsipras and his Syriza party, who had gambled all on the outcome.

In a statement on his blog, Mr Varoufakis said the vote was a "unique moment when a small European nation rose up against debt-bondage", but that some eurogroup leaders had made clear a fresh agreement with creditors would be more likely if he was not part of future talks.

He said he was quitting as finance minister to help Mr Tspiras "exploit, as he sees fit, the capital that the Greek people granted us through yesterday's referendum", adding: "I shall wear the creditors' loathing with pride."

European Commission vice president Valdis Dombrovskis insisted the "stability of the euro area is not in question" and authorities stand ready to "do whatever is necessary".

He told a press conference in Brussels: "One thing is clear - the place of Greece is and remains in the eurozone. To solve this very difficult situation all sides need to work responsibly for the sake of Greece's people."

Mr Dombrovskis said the European Commission did not currently have a mandate to reopen negotiations with Greece.

He said: "So far, the eurogroup has not given a mandate to the Commission to start the negotiations."

Greek employment minister Rania Antonopoulos said leaving the eurozone would be the "worst possible outcome".

She told BBC Radio 4's Today programme: "There are still 48 hours, there is still this week. We will push as much as possible for an outcome, a result of these negotiations, that does not obligate Greece to go in that direction."

Klaus-Peter Willsch, who sits in the German parliament as a member of Mrs Merkel's CDU Party, said Greece should leave the euro.

He told the programme: "I think it's not possible that the debtor blackmails the creditor. They try to have a living far beyond the economic possibilities and send the bills for that to other countries' taxpayers, which is not fair and not a way for the future.

"The sooner you stop throwing more money in a barrel without a bottom, you stop losing more money," he added.

Mayor of London Boris Johnson said: "Greeks have shown they can't be pushed around. EU bluff called. EU political class told Greece to vote yes - and Greeks told them to bog off."

Britain's ambassador to Greece, John Kittmer, joined the Whitehall meeting by video-link, reporting that banks remained closed but cash machines in the country were still dispensing notes and there did not seem to be queues developing of Greeks seeking to remove their savings.

Also taking part in the meeting were the UK representative in Brussels by video-link, Business Secretary Sajid Javid, Work and Pensions Secretary Iain Duncan Smith, Europe Minister David Lidington and Minister for Government Policy Oliver Letwin.