Business chiefs have warned they would struggle to fill key jobs under proposals by government advisers to tighten the visa rules for non-European workers and to charge them a “skills tax”.

In moves to cut migration numbers and tackle the undercutting of some British workers’ pay, the Migration Advisory Committee called for companies to be banned from recruiting staff from outside Europe on salaries of less than £30,000.

Its report comes as ministers search for ways of curbing net migration levels – currently more 330,000 a year – without hampering economic growth.

It found evidence that non-EU nurses and doctors were being paid £6,000 less than their British equivalents, while foreign secondary teachers earned £2,000 less.

It urged Theresa May, the Home Secretary, to levy an annual “immigration skills charge” of £1,000 for every skilled non-European worker they hired – a move which would raise £250m a year for training Britons.

In a series of measures which could see the flow of migrants cut by more than 30,000, it also backed tougher restrictions on companies transferring foreign-based staff to the UK.

But the Institute of Directors said the plans would hit thousands of firms and “send a message around the world that the UK is no longer open to international talent”.

Attempts to tighten rules for skilled workers are already proving highly contentious.

Ministers are facing demands to rethink plans to force non-EU migrants to prove they are earning at least £35,000 after five years in the country – or risk being ordered out of Britain.

The committee’s recommendations came in a review into “tier two” visas, which are issued to skilled migrants from outside the European Economic Area. Currently they must be taking up a job with a salary of at least £20,800, although there are higher thresholds from some jobs. In 2014, 151,000 people came to Britain by this route.

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

The committee called for the threshold to be raised to £30,000, although it said the increase should be phased in to allow employers to adjust recruitment plans.

Prof Sir David Metcalf, the committee’s chairman, suggested it be phased in over three or four years for professions such as nursing to coincide with a drive to train more British nurses.

Nurses have currently been exempted from the cap by Ms May to avoid a recruitment crisis. The committee will report next month on whether the end the temporary exemption.

The advisers said they strongly supported the skills charge to encourage employers to look closer to home to fill jobs vacancies. It suggested a yearly levy of £1,000 for each tier two migrant taken on by a British firm.

Prof Metcalfe said: “Skilled migrant workers make important contributions to boosting productivity and public finances, but this should be balanced against their potential impact on the welfare of existing UK residents.”

The committee also backed tighter restrictions on “intra-company transfers” by raising the minimum salary for visas to £41,500. Indian IT workers are said to account for more than 90 per cent of such migrants.