Sir James Dyson, one of Britain’s most prominent inventors and business leaders, has described Theresa May’s plan to expel international students on graduation as a short-term vote winner that will harm the economy by losing the UK valuable ideas from the brightest foreign minds.

The home secretary announced last month that she wants the Conservatives to make a manifesto commitment to force students from outside the EU to leave the UK and apply for a new visa from abroad once they have completed their degree.

Dyson echoes criticism of the proposal from the academic and scientific communities, saying that it will make a shortage of scientists and engineers worse.

“Our borders must remain open to the world’s best,” he writes in the Guardian. “Give them our knowledge, allow them to develop their own, and permit them to apply it here on our shores. Their ideas and inventiveness will create technology to export around the world … May’s immigration plans simply force the nimble minds we nurture to return home and fuel competition from overseas. Why would they return? Often they hail from emerging economies and nations that respect science and engineering.”

The Campaign for Science and Engineering said the proposal was at odds with the government’s commitment to make Britain the best place in the world to do science.

Immigration is shaping up to be a key election battleground, with the Conservatives particularly wary of Ukip’s impact on their vote.

Present rules give overseas graduates up to four months to find a suitable job before leaving the UK, a window some already viewed as too short and less than the 12 months offered by the likes of the US, Australia and Canada.

Dyson, who is best known as the inventor of the Dual Cyclone bagless vacuum cleaner, said he accepted there may be an immigration problem, but that May’s plan was “a short-term vote winner that leads to long-term economic decline”.

Last November, the prime minister, David Cameron, praised Dyson as “a great British success story” after the company announced it was investing a further £1.5bn into research and development to create future products, which would create up to 3,000 jobs in the UK.

Dyson says, however, that the homegrown postgraduate population is “painfully thin” and that with nearly 200,000 international students researching technology at British universities, that is “200,000 ideas and inventions to lose”.

He writes: “Yes, these students net Britain nearly £7bn each year [in fees]. But sending them home with new technology developed here presents very good value to our competitor nations. Instead our education system should be a tool to import the world’s greatest minds. And, most importantly, to keep them here, so that it is our economy – and our culture – that benefits.”

He said that the company he founded had moved assembly to Malaysia 13 years ago because of insufficient government backing for manufacturing, and he questioned whether it was now “falling dangerously out of love with conceiving technology too”.

Universities UK has warned that May’s proposals risk increasing the perception that Britain does not welcome international students. In 2011-12, the number of overseas students taking up places at English universities fell for the first time in 29 years.

A Conservative party spokesman said: “We are still deciding what will be in our manifesto and will outline its contents in due course.”