The Home Office is drawing up contingency plans to cope with a possible big increase in immigration from Greece if the euro collapses.
EU nationals are largely entitled to work anywhere in the single market.
But Home Secretary Theresa May told the Daily Telegraph “work is ongoing” to restrict European immigration in the event of a financial collapse.
Labour MP Denis Macshane said Mrs May was “stoking up tension”, and restrictions were impractical.
The Home Secretary said “trends” were being examined to see whether immigration was rising from countries with stricken economies.
She said if the single currency broke up, people looking for work abroad may see Britain as an attractive alternative as it is a non-eurozone country.
Asked whether emergency immigration controls were being considered, Mrs May said: “It is right that we do some contingency planning on this [and] that is work that is ongoing.”
She said there was no evidence that migration was on the rise, but it was “difficult to say how it is going to develop in coming weeks”.
BBC political correspondent Robin Brant said the government had some room for manoeuvre because there are rules in place for extreme situations which allow for some temporary restrictions on immigration.
Details of the contingency plans followed yet more turmoil in the single currency after Spain’s fourth-largest bank, Bankia, asked the government for a bailout worth 19bns euros ($24bn; £15bn).
European markets fell again as the value of the euro slid.
But in January, a report from the government’s official advisers on migration, the Migration Advisory Committee, said EU migration had had “little or no impact” on the native employment rate.
Former Labour Europe Minister, Denis MacShane, says he was worried by Mrs May’s comments.
“Every government department has contingency plans for most things. It does frighten me a bit because Mrs May is stoking up tension and of course, if we ban every Greek from coming into Britain, the Greeks will ban every Brit from going into Greece – that’s a great start to the holiday season.”
Mrs May also told the Telegraph work is under way to deny illegal immigrants access to work, housing, services and even bank accounts.
“The aim is to create here in Britain a really hostile environment for illegal migration,” she said.
“What we don’t want is a situation where people think that they can come here and overstay because they’re able to access everything they need.”
Prime Minister David Cameron said last week the eurozone must decide soon whether it wants to stay together or break-up.
He told MPs: “If it wants to carry on as it is it has to build a proper firewall, it has to take steps to secure the weakest members or it has to work out it has to go in a different direction.
“It either has to make-up or it is looking at a potential break-up. That is the choice they have to make and it is a choice they can not long put off.”
Source: BBC News UK