Home Secretary Theresa May said contingency plans are being made in case millions of economic migrants flee Greece to seek better opportunities abroad.
Her statement comes amid growing alarm in the eurozone as the worldwide economic downturn continues to cast its long shadow over the single currency.
The fear is that Greece or other states could leave the 17-country bloc in a sudden move, spelling millions of job losses and forcing people to look abroad for work.
May said: "As in every part of Government, it is right that we do some contingency planning on this. That is work that is ongoing."
Her comments came as Christine Lagarde, the head of the International Monetary Fund, said she had more sympathy with children in Africa than those in Greece who are "trying to escape tax".
Asked in an interview whether she worried about the economic and social impact of austerity in the Mediterranean country, she 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."
In London, hundreds of anti-cuts campaigners yesterday protested outside the house of deputy prime minister Nick Clegg over his backing of the Government's austerity spending plans.
Disabled activists with UK Uncut chained wheelchairs at both ends of the street in Putney where he lives. The group is staging protest "street parties" in 10 UK cities, and said it was targeting Clegg as "one of the architects of austerity".
Jean Sandler, 42, a UK Uncut supporter, said: "The cuts are a political choice of this Government and the Cabinet of out-of-touch millionaires. They are not necessary.
"No one voted for Cameron and Clegg's disastrous plan that means that we end up paying for the banks' crisis. The cuts are getting personal and so are our protests."
Elsewhere in the eurozone, the economic clouds were darkening further over Spain, with the troubled Bankia bank calling for a £15 billion government bailout.
The Spanish Government has promised Bankia the money, an amount far higher than it envisioned when it effectively nationalised the bank this month.
Bankia president Jose Ignacio Goirigolzarri tried to calm fears about its future, saying it would emerge as a solid financial entity.
Bankia and its parent group BFA are to sell a large real estate portfolio and a package of companies to turn itself around, he said.
However, there are fears that the cost of rescuing the country's vulnerable banks could overwhelm its finances.