Britain faces exclusion from one of the glowing successes of European Union membership: a university study programme that has benefited tens of thousands of British young people and many more from the EU visiting Britain.

Under the Erasmus scheme, British students can study at European universities for between three months and a year, and European students in the UK. But after Brexit, says the scheme’s UK director, Ruth Sinclair-Jones, “we face a sad moment of uncertainty, after 30 years of this enrichment of so many lives”.

The end of British participation in the scheme would be “a devastating tragedy” according to those who founded and administer it.

Exclusion from Erasmus would also have what one vice-chancellor called “a stunning impact” on university finances, alongside the crisis facing funds for science, research and other grants. There are 120,000 students from EU countries at UK universities, of which 27,401 are through Erasmus with their fees paid by the EU.

Sinclair-Jones said that those now in the scheme or applying for next year should be unaffected, but “in the long term, it’s an unknown situation. We will continue with our plans until 2017 and try to minimise the anxiety. But after that we have to wait for an outcome.”

Erasmus, named after the Renaissance humanist philosopher, was launched by the European commission in 1987, since when more than two million young people have benefited from EU-funded grants to study in 27 countries.

“In Britain, interest has accelerated,” said Sinclair-Jones, who is based at the British Council, which operates the UK end of the programme with an organisation called Ecorys. “In 2007 we had 7,500 applications to study in Europe. By 2013, that had risen to 15,000.”

Ironically, Erasmus had its genesis in the UK: its founding father was Dr Hywel Ceri Jones, one of the first British diplomats to the EEC in Brussels during the 1970s, having – at Sussex University with Professor Asa Briggs – set up Britain’s first European Studies department. Pilot schemes from 1976, he said last week, “were inspired by the idea that the internationalisation of study had to apply to all disciplines, not just languages. So we brought in the scientists, social sciences and arts.”

Ceri Jones, who went on to become director-general for education and later social policy at the European commission, said: “Erasmus will still flourish in Europe, but UK universities have been a powerful magnet because of the English language.

“I feel bereaved by Brexit, and if it leads to the end of freedom of movement and exclusion of the UK from Erasmus this would be devastating – a tragedy of staggering proportions for universities throughout the country, for the structured internationalisation of our academic institutions, which is what Erasmus is all about.

“We are talking about enriched and changed lives, lifelong friendships – since the programme was launched, so many Erasmus babies have been born to couples who met through Erasmus.”

Sinclair-Jones added that “98% of our students report having hugely benefited from their time in Europe. Meanwhile, Erasmus has hosted European students and internationalised our own academic institutions so as to open young people’s minds, broaden horizons.”

Considering the options open to negotiating a way to keep Britain in the scheme, the Universities UK group, which liases between academic institutions receiving and sending Erasmus students, points out that Norway is a participant but, says one of its officers: “Norway has accepted freedom of movement as part of its relationship to the EU, and we don’t know if Britain will do that.”

However, he says: “The Swiss had their referendum limiting freedom of movement and were told they are therefore out of Erasmus. Switzerland has now initiated its own scheme, but this costs a lot of money – and raises the issue that only better-off families can be part of it. The great thing about Erasmus is that it made the experience and opportunity available to every student, whatever their family means.”

Universities UK calculates that fees paid by EU students totalled £600m in 2014-15, and that students from Europe spend £1.49bn a year in off-campus costs, such as rent and subsistence.

Ceri Jones’s alma mater, Aberystwyth University, is one of the most international universities in Britain but the acting vice-chancellor, Professor John Grattan, said last week that a tenth of those from Europe who had applied for Erasmus places pulled out the day after the Brexit vote, and the same number since. “I won’t hide it from you that Brexit poses a challenge to the university,” Grattan said during a graduation ceremony. “Over 100 European students have withdrawn their applications to us at this point, 50 by the end of Friday on Brexit day. That’s a stunning impact on our finances.”

Grattan, a volcanic geologist, added: “The numbers of our own 18-year-olds coming to universities is declining and we’re doing very well in making up the shortfall by competing for international students. But Brexit is creating anxiety … We’re an international university in the most Europhile town in Britain, and I need to tell our European students we want them, and re-assure my European faculty they’re welcome here.”

With regard to the finances, he added: “We currently receive £37m in European research funding with a bid just in for another £18m. Research is not something you can switch on and off. We need some certainty – we need to know whether or not we’re riding a bicycle over a cliff.”

One of the universities most active in receiving and sending students through Erasmus is Grattan’s alma mater, Sheffield, where three years ago the university and its students’ union launched a campaign called “we are international”.

Dominic Trendall, president of Sheffield’s student union, said: “Over the last couple of weeks we’ve had to let people in Europe know they’re welcome, that we’re not part of this racist culture and a better university for the fact that people come here from abroad; it’s very depressing that we’ve had to do it.

“Erasmus is irreplaceable by other international schemes,” said Trendall, “and the loss of funds knocks on to higher fees – it’s all connected.”

“We’re a European country,” said Sinclair-Jones, “and Erasmus has become part of the rich cultural relations we must keep with Europe. I very much hope the UK can negotiate a deal that keeps us in full membership of the programme. I haven’t given up on this yet. I’m not ready to accept this blackness until we’re right there in it.”