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Theresa May’s immigration policy came under fresh strain today as experts warned that the minimum salary requirement for a non-EU migrant could top £60,000 for the first time.

Businesses and the British Medical Association said the “out-of-date” and “arbitrary” system must change or they would be “banging their heads” to recruit desperately needed doctors and skilled workers.

Earlier this week the Evening Standard revealed that Health Secretary Jeremy Hunt and Business Secretary Greg Clark have lobbied No 10 to relax the rules, to no avail.

Under a system created by Mrs May when she was home secretary, a minimum salary for visa applicants goes up automatically whenever the number of applications goes above an annual quota of 20,700 visas.

Madeleine Sumption, director of the Migration Observatory at the University of Oxford, said there was evidence that demand this year will be “much higher”, which would push up the earnings requirement, which has already risen from £30,000 to £50,000.

A rise to £60,000 or £70,000 would limit applications to workers falling in the top five per cent of UK earners, effectively limiting recruitment to highly paid occupations and ruling out many mainstream employers. “The fact that the cap has already been hit this April suggests that demand this year could well be much higher than in the past few years,” said Ms Sumption. “That would mean higher salaries.”

Jonathan Portes, professor of economic and public policy at King’s College, London, said it was a “crazy system”, addding: “The only point of a numerical cap is to stop us letting in skilled people that somebody wants to hire.”

Mark Hilton, director of immigration and employment policy at business group London First, said the system for Tier-2 visas was “out-of-date, opaque and stopping us from hiring skilled people the UK desperately needs”.

He urged: “A first step would be sorting the arbitrary caps that more and more London businesses are banging their heads against.”

The BMA, plus NHS Employers and 12 royal colleges and trade unions united to send a letter to new Home Secretary Sajid Javid asking for the cap to be reduced. Dr Chaand Nagpaul, BMA council chair, said arbitrary caps were “inexplicable and threatening patient care and safety”.

The current system was devised to help drive down net immigration to 100,000. The quota was used up for five months in a row, causing the minimum salary to surge from £30,000 to £50,000 and briefly touch £60,000.

Ms Sumption said it was impossible to predict how high the salary requirement might go. It could “hop around” unpredictably, making it harder for firms to recruit, or even hit £100,000.

A Home Office spokesman said: “The Government fully recognises the contribution that international professionals make to the UK. However, it is important that our immigration system works in the national interest, ensuring that employers look first to the UK resident labour market before recruiting from overseas. "When demand exceeds the monthly available allocation of Tier 2 (General) places, priority is given to applicants filling a shortage or PhD-level occupations. No occupation on the Shortage Occupation List – which is based on advice by the independent Migration Advisory Committee – has been refused a place.”

Under the rules, a points system that rewards higher pay is used whenever visas are in danger of running out.

