The Home Secretary has told her EU counterparts that Britain is not prepared to join any “burden sharing” as tens of thousands of people cross in to Europe, The Daily Telegraph can disclose.
Italy, where the refugees are arriving on a daily basis, has urged its EU partners to help ease the pressure by accepting some of the migrants.
But at a meeting of her justice and home affairs counterparts last week Mrs May said Britain will only offer support to Italy to help deal with the issue there.
She will repeat her firm stance when the EU Justice and Home Affairs Council meets again next month.
It came as British MEPs warned migrants could head for Britain because it is seen as a soft option and called for action to stop camps building up at Calais.
A borderless scheme on mainland Europe is already under threat amid growing tensions over the plight of the fleeing refugees and migrants.
More than 25,000 Tunisians have arrived in Italy since unrest there and thousands of Libyans are expected to try to head for Europe. More than 14,000 crossed in to Tunisia in the last two weeks alone.
More migrants from sub-Sahara Africa are also likely to cross because Col Muammar Gaddafi is no longer stopping them in Libya.
A row developed between France and Italy earlier this week when the former stopped a train carrying Tunisians migrants at the border.
Under the so-called Schengen agreement, citizens in 25 EU nations are allowed to travel across borders without having their passports checks.
The UK and Ireland are not part of the agreement and control their own borders.
However, Italy has caused angry among its neighbours by handing temporary permits to more than 25,000 Tunisians after other EU countries declined to help accommodate them.
It effectively gives them unobstructed travel around the union.
Gerard Batten, the Ukip MEP for London, said: “People are going to gravitate to Britain.
“Britain is top of the list because we have one of the most generous welfare benefits systems and we are famous for being a soft touch.
“I don’t have any confidence in the authorities doing anything to stop them coming in.
“”There is a human crisis, but the approach of giving people residence permits will make things permanent, rather than encourage people to return home when peace in Libya and the whole of north Africa finally returns.
“The problem here for us is the European borderless state.”
Richard Ashworth, the Conservative MEP for South East England, added: “The Calais authorities have recently taken action to remove the immigrants in the town intending to enter the UK.
“Both the French and British authorities need to remain vigilant to ensure this bottleneck does not occur again if large numbers of people from North Africa enter France.
“The sad days of squalid camps in the woods and British hauliers running the Calais gauntlet must not be allowed to happen again.”
The growing tensions in Europe has put the Schengen agreement under threat.
Along with France, the Netherlands, Belgium, Austria and Germany are understood to be considering reintroducing some border checks.
A Home Office spokesman said: “A common asylum system or new laws will not resolve the unprecedented influx of migrants at Europe’s Mediterranean border.
“Britain has offered Italy practical assistance to help maintain their border controls and asylum processes. Those seeking international protection are expected to claim asylum in the first safe country they enter. Those who have no genuine claim to protection should be returned to their home countries quickly.
“We retain the right to not opt into any agreement which will weaken Britain’s borders.”