“THEY are not, and never have been, immigrants.” So declared Enoch Powell of international students in an infamous speech against migration in 1968. Ending up to the right of Powell, who was as fierce a critic of immigration as they come, is an uncomfortable position. But that is where Theresa May’s government finds itself with respect to overseas students. As part of a plan to reduce the number of migrants, on October 4th Amber Rudd, the home secretary, announced new restrictions on foreign students, including tougher entry requirements for those going to lower-quality institutions. The proposal is merely the most recent attempt to deter foreigners from paying tens of thousands of pounds to study in Britain.

Since the turn of the century the number of foreign students in Britain has more than doubled (see chart). In contrast to Britain’s overall immigration trend, growth has come not from Europe but from the rest of the world. Chinese students are by far the biggest group, numbering 89,540 last year, up from 47,740 in 2004. The steep fees paid by non-EU citizens have made higher education an important British export. By one estimate foreign students contribute £7 billion ($8.6 billion) a year to the economy in fees and living expenses.

Yet in the past few years the growth has stalled. To find out why, visit any student common room. An American PhD student at Cambridge University complains that acquiring a visa for her doctorate was more onerous than when she studied in Britain a decade ago. This time she had to list every trip she had taken outside America since the age of 18. Applicants have to prove they have more money than they used to: £9,135 in the bank plus their tuition fees, up from £7,380 last year. And the government has introduced an annual “immigration health surcharge” of £150. The doctoral student says she gets e-mails almost weekly from the university citing new requirements it faces with regards to its foreign students.

The government has also removed provisions that allowed students to stay on after graduation to seek work. In 2012 it abolished a visa which allowed those who had completed degrees in Britain to remain in the country for two years without the firm offer of a job. The withdrawal of this perk put off many South Asian students, thinks Ruth Owen Lewis, director of the international office at Aberystwyth University. The number of Indian students, which soared from 14,625 in 2004 to 39,090 in 2011, has fallen to 18,320 since then.

The recent rhetoric may exacerbate this trend. Following Ms Rudd’s announcements, one Indian newspaper advised those considering studying in Britain to revisit their plans. Others see it differently: William Vanbergen, head of BE Education, a consultancy in China that advises those wishing to study abroad, says that some Chinese parents imagine that Brexit will mean fewer refugees and terrorists sneaking into Britain, making the country less dangerous for their offspring.

Other countries spy an opportunity. Australia and Canada, popular alternatives for Asian students seeking an English-language education, offer (limited) chances to stay and work, making them attractive destinations. Australia has simplified its student visa system to boost its appeal. Germany is offering more courses in English. And since 2014 public universities there have largely abolished tuition fees, including those for foreigners. This month the Irish government revealed plans to encourage more foreign students. “Everybody is doing the exact opposite to us,” laments Ms Owen Lewis. While the number of foreign students in Britain has stalled, in other countries it is zipping up. In Australia it increased by 11% last year.

Nor does the crackdown look politically necessary. A YouGov poll last year found that students were the most popular group of migrants among voters, three-quarters of whom thought their numbers were about right or should be higher. Even supporters of the right-populist UK Independence Party were keen on them. Reducing immigration in general will hurt Britain’s economy; barring fee-paying students is a particularly damaging way to do it.