More than 40,000 skilled migrants a year are to lose their right to work beyond five years in Britain, in a move towards creating a temporary "guestworker" migrant labour force in the UK.

The home secretary, Theresa May, will tell MPs on Wednesday that she is breaking the link between migration and settlement for the first time, by taking away the right to remain in Britain for more than five years from any migrant worker earning less than £35,000 a year.

The announcement comes as university vice-chancellors warned ministers that their policy of curbing the number of overseas students is at odds with attempts to boost economic growth. The action group Universities UK said it was wrong to classify students as migrants when 79% of them go home after five years and they should be removed from the politically sensitive net migration figures.

"They should do this because the majority of students simply come here, study, and then leave," said Professor Eric Thomas, president of Universities UK.

The move to break the link between migration and settlement comes after Home Office figures showed the immigration cap on skilled workers has been under-subscribed by 50%, with only 10,000 out of a limit of 21,700 work visas expected to be issued in the year to 1 April.

The Home Office's migration advisory committee said that nearly three times as many overseas skilled workers – 29,700 – from outside Europe have come to work in Britain in the past year through the intra-company transfer scheme, which is exempt from the cap.

Ministers hope changing settlement rights for skilled workers will put plans back on track to cut net migration from its current 250,000 a year to "tens of thousands" by the next general election. They believe the £35,000-a-year earnings threshold will ensure only the "brightest and the best" migrants settle in the UK. But critics say it will simply mean only the wealthy and the comfortable are able to come and live and work in Britain permanently.

"Ministers accept that our economy needs skilled migrants to come and work at levels below £35,000 a year, but have decided that even if they work hard, pay their taxes, and play by the rules, they will be forced to go home after five years," said Matt Cavanagh of the thinktank the Institute of Public Policy Research.

"This makes no sense in economic terms, will cause big problems for employers, and is unfair on individual migrants. It could also discourage the 'brightest and best' from coming here in the first place. The majority of working migrants don't stay permanently anyway, but they value the option, and if Britain no longer offers it, they may go elsewhere."

"Guestworker" policies, such as those applied in Germany in the 1970s and 1980s, were notoriously unworkable, he said. "The pattern is always the same: the policy is quietly abandoned when it becomes clear that there is no way to enforce the new rules." He said instead of removing settlement rights it would make more sense to provide financial incentives for migrants to return home.

The migration advisory committee has estimated that the current level of 60,000 skilled workers settling in Britain each year could be reduced to 20,000 by adopting a £35,000 earnings limit.

May is expected to announce some exceptions to the limit, including a lower earnings threshold for jobs in shortage or at PhD level.

The changes in settlement rights will also include a new rule removing the rights of overseas nannies, cooks and other domestic workers to settle in Britain after five years. In 2010, 15,700 visas were issued to foreign domestic workers from outside Europe. The new rules mean that in future they will only be able to work for foreign visitors and their period in Britain will be restricted to six months.