The Government is making contingency plans to cope with a potential increase in immigration should the euro currency collapse, the Home Secretary has revealed.
There is rising concern that Greece will be forced to abandon the euro after five years of recession, two bailouts and rising anger among voters over draconian austerity measures.
Political leaders in the European Union and Germany have said the euro will survive even if Greece leaves - despite warnings that it would start a domino effect among other troubled nations and cause a deep recession.
As EU citizens, Greeks are entitled to live and work in the UK and although there is no evidence of increased migration at present, the Home Secretary said it was "difficult to say how it is going to develop in coming weeks".
Theresa May told The Daily Telegraph: "It is right that we do some contingency planning on this (and) that is work that is ongoing."
There is strong support for anti-austerity parties in Greece ahead of a general election on June 17 after another vote earlier this month resulted in political deadlock.
The latest opinion polls suggest the conservative New Democracy party, which would continue to impose austerity, is extending its lead over the left-wing Syriza party, which claims it would reverse spending cuts.
In a warning to Greeks ahead of the election, the International Monetary Fund (IMF) boss Christine Lagarde said it was time they paid for the mistakes of the past.
Asked by The Guardian if she was concerned about Greeks who are suffering from life-changing austerity measures, Ms Lagarde said: "No, I think more of the little kids from a school in a little village in Niger who get teaching two hours a day, sharing one chair for three of them, and who are very keen to get an education.
"I have them in my mind all the time. Because I think they need even more help than the people in Athens.
"I also think about all those people who are trying to escape tax all the time. All these people in Greece who are trying to escape tax."
Social structures continue to deteriorate in Greece with claims by chemists that they are running out of medicine after a government funding freeze.
Sky News has also found how some Greeks have resorted to rummaging in dustbins for food.