BRITAIN’S private schools are one of its most successful exports. The children of the well-heeled flock to them, whether from China, Nigeria or Russia: the number of foreign pupils rose by 1.4% in the last year alone. One headmaster recently asked a room full of pupils whether they flew business class to Britain. Only a few hands went up, suggesting they were not quite as cosseted as he had thought. Then a boy explained: many of the pupils fly first class instead.

Yet foreign students, whether educated in British private schools or elsewhere, are decreasingly likely to go to English universities. According to the Higher Education Funding Council for England, 307,200 overseas students began their studies in the country in 2012-13, down from 312,000 two years earlier and the first drop in 29 years. Student numbers from the rest of the EU fell—probably a result of the increase in annual tuition fees in England from £6,000 ($10,000) a year to £9,000. But arrivals from India and Pakistan declined most sharply.

In contrast to the visa regime for private schools, which is extremely lax (the Home Office counts private schools as favoured sponsors) student visas have been tightened. Foreign students used to be allowed to work for up to two years after graduating. They now have only four months to find a job paying upwards of £20,600 if they want to stay in Britain.

This change was intended to deal with sham colleges that were in effect offering two-year work visas. But it seems to have put off serious students too. Nick Hillman of the Higher Education Policy Institute says the government has sent unclear messages about the sort of immigration it wants to restrict. An emphasis on holding down net immigration deters young Indians and Pakistanis in particular. Australia and America, which have more relaxed entry criteria for students, are becoming more favoured destinations. Colin Riordan, Cardiff University’s vice-chancellor, adds that Britain’s student-visa regime has become more onerous and fiddly overall.

As a result, Britain is losing out to other countries in the contest for talent—an oddity, given how often the prime minister bangs on about the “global race”. Its unwelcoming stance will harm its long-term prospects. And the drift of foreign students from leading British private schools to American colleges may have another, somewhat happier, consequence: America might become rather better at cricket.