Vince Cable, the business secretary, has criticised the inclusion of overseas students in the UK’s net migration target as “irrational” and “potty” and admitted ministers are “frankly struggling” to balance the politics of immigration with the economic benefits foreigners bring to Britain.

Universities have long campaigned for international students to be exempted from the Conservative party’s drive to cut net migration to the “tens of thousands”, arguing this creates the impression that overseas students are not welcome in Britain and risks damaging the UK’s ￡8bn a year education export industry.

But Mr Cable – who has in the past angered Tory colleagues with salvos against their immigration cuts – was careful to blame the UN, rather than fellow ministers, for what he sees as a statistical anomaly.