Foreign graduates could face being sent back to their home countries under plans to “move towards zero net student migration” reportedly being considered by Home Secretary Theresa May.

Students from non-European Union countries would have to subsequently apply for a work visa while abroad in order to continue living in the UK after finishing a course of study, The Sunday Times reported, instead of being able to apply for one while still on British soil.

A source close to the Home Secretary told the newspaper: “Making sure immigrants leave Britain at the end of their visa is as important a part of running a fair and efficient immigration system as controlling who comes here in the first place.”

Mrs May is also pressing for the power to be able to penalise colleges and universities that would have low success rates in ensuring the departure of foreign graduates and to deprive them of their right to sponsor overseas students, the source added.

Under current rules most students can apply for a work visa while still living in the UK, rather than having to leave the country to apply for one before potentially returning.

10 things immigration has done for Britain Show all 10 1 /10 10 things immigration has done for Britain 10 things immigration has done for Britain The Mini The 1959 classic, that is, perhaps our greatest piece of industrial design, a miracle of packaging and revolution in motoring. Its genius designer was Sir Alec Issigonis, who was an asylum seeker. His family, Greek, fled Smyrna when Turks invaded this borderland in around 1920, and he wound up studying engineering at Battersea Polytechnic. He went on to create that most English of motor cars, the Morris Minor, as well as the Austin-Morris 1100, all much loved products of his fertile imagination. Getty Images 10 things immigration has done for Britain Marks and Spencer Once upon a time there was no M&S in Britain, difficult as that may be to believe. We have one Michael Marks to thank for our most famous retailer, and he was a refugee from Belarus, arriving in England in about 1882, and soon after set off to flog stuff around Yorkshire. He eventually teamed with Thomas Spencer to create the vast business we know today. Getty Images 10 things immigration has done for Britain Thunderbirds And many other TV shows created, funded and otherwise produced by that largest of larger-than-life characters, Lew Grade (also a world class tap dancer). The man who dominated commercial television gave us memorable entertainment such as The Prisoner, the Saint and brought the Muppets to Britain (a sort of fuzzy felt wave of immigration), as well as puppet shows where you could see the strings. All this from a penniless Jew from Ukraine, born Lev Winogradsky, who escaped the pogroms in Ukraine with his family in the 1890s. His nephew Michael Grade has also done his bit for British television. Rex Features 10 things immigration has done for Britain The House of Windsor Or the House of Saxe-Coburg-Gotha until George V prudently rebranded the family during the First World War. Well, our royals are a pretty German bunch, as well as having various types of French and other alien blue blood coursing around their veins. ‘Twas ever thus. There was William the Conqueror, Norman French, who certainly broke the immigration rules; William of Orange, a direct import from Holland; the Hanoverian King Georges, the first barely able to speak English; Queen Victoria, who married a German, Edward VII, who couldn’t stay faithful to his wife, a Danish princess; George V wed another German princess; Edward VIII married an American (though she hardly visited England and prompted his emigration and exile); and the Queen is married to man born in Corfu. The embodiment of the British nation, to many, but one thinks of them as quite multicultural really. Getty Images 10 things immigration has done for Britain I Vow To Thee My Country Our most patriotic hymn was the product of a man named Gustav Holst (pictured), born in Cheltenham, but of varied Swedish, Latvian and German ancestry, who adapted part of his suite The Planets to put a particularly stirring and beautiful poem to music, just after the Great War. As the second verse has it, “there's another country/I've heard of long ago/Most dear to them that love her/most great to them that know”. Imagine if the Holst family had been kept out because the quota on musical European types had been reached. Creative Commons 10 things immigration has done for Britain Curry and Cobra Chicken Tikka Masala is, so they say, a dish which not only the most popular in Britain but specifically designed to cater for European tastes. For that we probably have to thank an Indian migrant, Sake Dean Mahomed, who came from Bengal to open the first recognisable Indian restaurant, the magnificently named “Hindoostanee Coffee House”. History does not record if a plate of poppadoms and accompanying selection of pickles and yoghurts were routinely placed on the table for new diners, but we do know that we had to wait until 1989 to taste the ideal lager for a curry - Cobra. That brew was brought to us by Karan (now Lord) Bilimoria, a Cambridge law graduate who hailed from Hyderabad. Getty Images 10 things immigration has done for Britain That big red swirly sculpture at the Olympic Park Or Orbit, to give it its proper name, the work of Anish Kapoor, who arrived in 1973 from India and had the artistic imagination to fill a power station. Getty Images 10 things immigration has done for Britain The Sun Love it or hate it, and many do both, this has been a symbol of much that is successful and a lot that is awful in British journalism since its inception in 1969. In its turn it spawned the Page 3 Girl and some nastily xenophobic headlines. All the stranger when you consider its creator was, of course, Rupert Murdoch, born 11 March 1931 in Melbourne, Australia. Getty Images 10 things immigration has done for Britain Marxism OK, Karl Marx’s philosophy was not much of a gift to the world, but for a while it seemed like a good idea. Though we might not dare admit it, Marxism still has a few insights to offer to anyone wanting to understand the workings of capitalism, though too few to excuse everything that was done in its name. Born in Germany spent much time in the British museum and the British pub, buried Highgate Cemetery. Oddly, his ideas never really caught on in his adopted homeland. Getty Images 10 things immigration has done for Britain The NHS They came from many, many backgrounds, including Ireland, the Philippines, east Europe, the Indian subcontinent, and Africa, as they still do, but the contribution of the black nurses who came to the UK from the Caribbean to heal and care for is a debt of honour that must be recognised. It so sometimes forgotten that it was Enoch Powell, then Minister of Health (1960-62), who campaigned to recruit their skilled nurses to come and work over here. One abiding legacy we can thank Enoch for. Getty Images

Mrs May has repeatedly clashed with Liberal Democrat Business Secretary Vince Cable - whose department has responsibility for universities - about foreign students as he claims that tough rules could discourage them from choosing to study here.

A senior Lib Dem source said her plan could deprive the UK of highly-skilled graduates.

“Such a blunt instrument would not get our support,” the source said.

“The idea that you have people from abroad studying in this country and they become engineers or scientists of huge practical value to the economy and rather than have them stay here you immediately turf them out makes zero economic sense.”

Mrs May's plan emerged after Prime Minister David Cameron insisted that only the Tories can offer “competence” on dealing with immigration.

David Cameron claimed his government was fixing problems left by the Labour Party (Getty)

Mr Cameron and Mrs May plan to reduce net annual migration from hundreds of thousands to tens of thousands by the next election, however the Home Secretary stated on the Andrew Marr Show that the target is likely to not be met.

The Prime Minister claimed that his coalition government has addressed some of the problems inherited from the previous Labour administration that “let immigration get out of control” and seeks to pinpoint those living in the UK illegally before deporting them by revoking driving licences, the ability to open a bank account and have landlords check on the immigration status of their tenants.

Mr Cameron also stated an “absolute requirement” to make changes to the welfare state for migrants in the hope to cut down the numbers of people moving to the UK from within the European Union.

He said: “I came into office with a single-minded determination to turn all this around - and real progress has been made.