David Cameron is prepared to override Britain's historic obligations under EU treaties and impose stringent border controls that would block Greek citizens from entering the United Kingdom, if Greece is forced out of the single currency.

The prime minister told MPs that ministers have examined legal powers that would allow Britain to deprive Greek citizens of their right to free movement across the EU, if the eurozone crisis leads to "stresses and strains".

In an appearance before senior MPs on the cross-party House of Commons liaison committee, the prime minister confirmed that ministers have drawn up contingency plans for "all sorts of different eventualities".

The worst-case scenario is understood to cover a Greek exit from the euro, which could trigger further collapse of the already collapsed Greek economy and the flight of hundreds of thousands of its citizens who are currently entitled to settle in any EU country.

The prime minister said Britain is prepared to take measures to avoid a major influx of Greek citizens. "I would be prepared to do whatever it takes to keep our country safe, to keep our banking system strong, to keep our economy robust. At the end of the day, as prime minister, that is your first and foremost duty."

Asked by Keith Vaz, the Labour chairman of the House of Commons home affairs select committee, whether he would restrict the rights of Greek citizens to travel to Britain, the prime minister said he would be prepared to trigger such powers.

"I hope it wouldn't come to that," he said. "But, as I understand it, the legal powers are available if there are particular stresses and strains. You have to plan, you have to have contingencies, you have to be ready for anything – there is so much uncertainty in our world. But I hope those things don't become necessary."