David Cameron is to chair a meeting this morning in which he will review contingency plans already in place over Greece's decision to reject terms of an international bailout plan.
A Number 10 spokesman said: "The Greek people expressed a decisive view in yesterday's referendum. This is a critical moment in the economic crisis in Greece. We will continue to do whatever is necessary to protect our economic security at this uncertain time.
"We have already got contingency plans in place and later this morning the Prime Minister will chair a further meeting to review those plans in light of yesterday's result."
The Government has also issued travel advice for British tourists, warning banking services, such as credit card purchase and cash withdrawals, could become limited at short notice.
Greece's Prime Minister has called for 'a strong national front' as the country looks to negotiate a way out of the country's debt crisis.
Greece overwhelmingly rejected tough austerity terms set by international creditors.
Alexis Tsipras told Greek President Prokopis Pavlopoulos: "We must move forward immediately with negotiations.. a strong national front must be created to seek an immediate solution."
He is asking the president to convene a meeting of political party leaders.
Supporters of the Greek referendum's 'No' campaign have taken to the streets of Athens tonight to celebrate.
Waving Greek flags crowds gathered to celebrate in Syntagma square after the nation voted overwhelmingly "No" in a historic bailout referendum rejecting new austerity terms for fresh financial aid.
Greek Prime Minister Alexis Tsipras has said his country has made a "brave choice" after rejecting creditors bailout terms by voting 'No' in a crunch referendum tonight.
Tsipras who has led the 'No' campaign said the country will now go to the negotiating table with the goal of restoring its banking system and negotiating for "a plan of reforms".
Voters in Greece have rejected creditors bailout terms by voting 'No' in a crunch referendum on the country's debt deal.
With more than two thirds of the votes counted the nation has voted to reject the austerity terms demanded by the country's international creditors with more than 60% marking the "no" box on their ballot cards.
German Chancellor Angela Merkel and French President Francois Hollande have called for a special euro zone leaders' summit on Tuesday following the results of tonight's Greek referendum vote, officials have confirmed.
Greece's opposition leader Antonis Samaras has stepped down as leader of Greece's conservative New Democracy party.
The former Prime Minister said in a televised statement: "Our party needs a new start. As of today, I'm resigning from the leadership of New Democracy."
The 'No' vote is currently in the lead with 61% of the votes as counting in tonight's Greek referendum continues.
Greece referendum count so far 61% no
Prime Minister David Cameron is set to meet with advisers on Monday to assess the impact on Britain of the Greek referendum vote.
Votes are currently being counted in the country's crucial bailout referendum on whether to accept an austerity package from EU leaders, with early TV opinion polls putting the "No" vote narrowly ahead.
Chancellor George Osborne, who is due to attend the meeting with Cameron, Mark Carney, and other senior officials, has already said Britain would not be "immune" from the fall-out from the vote.
Speaking on the BBC1's Andrew Marr Show he said: "I don't think anyone should be in any doubt - the Greek situation has an impact on the European economy which has an impact on us.
"We cannot be immune from these developments."