The government should introduce a new visa that allows international students to work in the UK for a longer period after they graduate, university leaders say.

An enhanced post-study work offer is needed to send a more “welcoming” message to overseas students looking to study here, the Universities UK (UUK) said ahead of its conference this week.

Under the visa proposals, graduates would be sponsored by a university to gain work experience in the UK for up to two years on a more flexible basis than currently permitted by the tier 2 visa.

Employers could miss out on talented, skilled international graduates who help to fill skills gaps in the country – such as engineering, technology and medicine – if the new visa is not introduced, university leaders have warned.

They added that UK institutions could fall down the global league tables based on popularity with international students - the country is currently second - if changes are not made soon.

In 2012, the government scrapped the post-study visa - which allowed international students to work in the UK for two years after graduation - as part of a crackdown on abuse.

Countries such as Australia, Canada and the US have seen the number of international students enrolled in education increase significantly (45 per cent, 57 per cent and 40 per cent respectively) since 2011, while the UK has seen an increase of only 3 per cent, UUK said.

These countries - which compete with the UK for international students - have more welcoming visa policies. For example, the US and Canada offers international graduates the opportunity to stay and work for up to three years after graduation, and Australia for up to four years.

Since the government scrapped the post-study work visa in 2012, international students in the UK have just four months following the end of their studies to find a job with a tier 2 sponsor.

The number of overseas students remaining in the UK to work following their studies has fallen significantly since the closure of visa. In 2011, the numbers of students transferring into work visas was 46,875, compared to 6,037 in 2016 – a fall of 87 per cent.

Professor Sir Steve Smith, vice-chancellor at the University of Exeter and chair of UUK's international policy network, told The Independent: “The UK as a country needs to make it absolutely clear that international students are absolutely welcome and the UK is open for business.

“Now is the time - when we are 29 weeks away allegedly from Brexit - for the UK to make a grand statement about welcoming a new era where global talent can come to this country, study, work afterwards and thereby deal with the number one issue of the UK economy which is productivity growth with those skilled workers entering the workforce.”

He added: “It is not Brexit in terms of the details of Brexit - it is the image, the hostile environment. I have never met anyone who I have talked to who isn't coming to the UK because of the details of Brexit - it's 'is the UK welcoming?’

“What we are trying to do is put our offer on a par with our major competitors and to say that despite the trials and tribulations of Brexit, the UK and its universities are one of the great systems in the world.

“We see no reason why that system should not be open to talented individuals. Especially when we now know that they come to study, maybe stay on a little bit to work, and then leave.”

If the visa is not introduced, Sir Steve added that the UK could lose its place in the world as a leading destination for international students – and a number of university courses in science and technology would struggle to recruit as they are largely dependent on international students.

Vivienne Stern, director of Universities UK International (UUKi), added that they could see “damage” to their research system if fewer international students decide to do masters and PhDs in the UK.

Under the visa, all higher education institutions registered as Tier 4 sponsors would be able to sponsor their graduates to search for and gain work experience for up to two years without restriction on job level or salary, and without an employer sponsorship requirement.

The call comes as a poll from Comres, of more than 4,000 British adults, reveals nearly three quarters (72 per cent) think international students should be able to stay in the UK post-graduation for at least a year to gain work.

Stephen Isherwood, chief executive at the Institute of Student Employers, said: "Allowing talented international students to work for a period post-study in the UK will help employers, large and small, to fill skills gaps."

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Yinbo Yu, international students’ officer at the National Union of Students (NUS), said: “We know these restrictive visa controls are putting international students off UK universities and believe it is a key step to making them feel welcomed in the UK again.

“However, it is clear the immigration system requires a complete overhaul, with international students removed from immigration legislation altogether.

“We must show that our global education system is protected post-Brexit and make clear that international students are not unwelcome visitors.”

A Home Office spokesperson said:

“There is no limit on the number of genuine international students who can come to study in the UK.

“We recognise the cultural and financial contribution which international students make to the UK which is why we have developed an excellent post-study offer.

“Graduates can stay if they get a graduate level job, get an internship or apply to set up a business in the UK.