Foreign students could be forced to leave the UK after their courses finish under tough new rules being considered by the British Home Secretary, reports say.

Theresa May wants the Conservative party's next manifesto include a pledge to make non-European Union graduates return home and apply for a work visa from abroad if they want to continue living in Britain, according to The Sunday Times.

At the moment most students switch easily to a work visa from within the UK. Under the proposal, universities and colleges would be fined and stripped of the right to sponsor foreign students if they fail to ensure that students left the UK.

A source close to the Home Secretary told the newspaper that Mrs May has warned the British Prime Minister David Cameron that failure to act on foreign students will make it impossible for him to hit his target of cutting net migration.

"Making sure immigrants leave Britain at the end of their visa is as important a part of running a fair and efficient immigration system as controlling who comes here in the first place," the source said.

"Theresa is pressing for the next Conservative manifesto to contain a policy that will make sure that anybody coming here on a student visa will have to leave the country in order to apply for a new visa of any kind."

"She wants to make the colleges and universities that sponsor foreign students responsible for ensuring their departure. And she wants to be able to fine colleges and universities with low departure rates and deprive the worst of them of their right to sponsor foreign students."

But senior Liberal Democrats warned Mrs May's plan could deprive the UK of highly-skilled graduates.

A senior Lib Dem source said it made "zero economic sense" and "such a blunt instrument would not get our support".

Economic impact 

Mrs May is also likely to face resistance from British Chancellor George Osborne, who encouraged Mr Cameron to ditch quotas for immigrants in his recent speech on EU migration because it would hurt the economy.

Writing in the Daily Express on Saturday, Mr Cameron said his government had addressed some of the problems inherited from a Labour administration that "let immigration get out of control".

"I came into office with a single-minded determination to turn all this around - and real progress has been made," he said.

"We put a cap on those coming here to work from outside the European Union - and we have seen the numbers fall significantly, close to levels last seen in the 1990s.

"Major work has been done to clamp down on the bogus 'colleges' that were really just a front for people to come here, with more than 800 of them shut down so far."

Official figures from the Office for National Statistics show that 121,000 non-EU students entered the UK in the year to June, but only 51,000 left, meaning 70,000 stayed behind in just one year, The Sunday Times says.

The business department there has calculated that the number of foreign students coming to the UK will rise by more than 6% a year up to 2020.