Ask most UK students what they think of when they hear the word ¡°Erasmus¡± and their minds will turn to the popular European Union programme that allows them to study in Europe, rather than the respected 16th-century philosopher.

It¡¯s no coincidence that the initials of the European Region Action Scheme for the Mobility of University Students spell out the name of the Dutch Renaissance humanist Desiderius Erasmus. His legacy of anti-dogmatic religious criticism and his extensive travel in a time of Catholic and Protestant warring across the Continent is a good match for the programme.

Since its formation in 1987, millions of Europeans have used the scheme to study abroad for between three and 12 months during their degrees. Those include more than 200,000 British students, with the numbers growing every year.

UK universities have also received thousands of Erasmus students. More than 170 British institutions are now involved in the programme, under which universities agree to recognise each other¡¯s courses so that the period students spend abroad counts towards their final qualifications.

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In a time when nationalism is on the rise not just in the UK but across Europe, we must invest in more cooperation, not less. Exchange programmes such as Erasmus work to erode the culturally rooted mistrust that sets nation against nation. Desiderius Erasmus understood this 400 years ago, when he travelled across the Continent to deepen his understanding and share ideas, but he was one of a very lucky few who had the means to do so. Another particular benefit of the Erasmus programme is that it does not make studying abroad an option only for more wealthy students. It¡¯s open to everyone, and students are supported for their travel and subsistence costs depending on need.

A number of EU member states, including the UK, were sceptical about the programme when it was first trialled, but its success is shown by how far it has been expanded. At its core is still the original study programme for university students, but interns, apprentices, volunteers, teachers and even professionals can now access opportunities through what is known as the Erasmus+ system.

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However, there is currently no certainty that the 18-year-olds who collected their A-level results last week will have the opportunity to benefit. The UK¡¯s participation in the scheme faces an unknown future after the vote to leave the EU, and Liberal Democrats have been campaigning to ensure that the government guarantees ongoing UK involvement in it.

In many ways, universities face more disruption from the result of the referendum than any other sector. Erasmus is just one programme in a long list of those affecting universities ¨C from immigration policy to Horizon 2020 membership ¨C on whose future the government will need to set out a position.

With a number of Brexit issues, the government has implied that it would rather use them as leverage in negotiations with the EU rather than commit to anything upfront. And, for the moment, everyone has in effect been told to keep calm and carry on: government responses to written parliamentary questions on the impact of the EU referendum currently come back saying ¡°nothing has currently changed¡±. But there is no excuse for government to be hesitant on the UK¡¯s desire to continue to be involved in Erasmus+, given the importance of what it represents.

It is worth saying that while the programme is the creation of the European Commission, it is not reserved for EU member states alone. Norway, Turkey and Iceland are all full members, with additional partnerships across the world. So even after the UK leaves the EU, there is no reason it should not continue to participate.

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Of course, the EU may also decide that it wants to use the UK¡¯s ongoing membership of Erasmus+ as a negotiating tactic, as it has with another non-member, Switzerland, after that country¡¯s vote in 2014 to restrict immigration from the EU. But, for our part, the UK should be using this opportunity to make a clear statement that we believe in Europe and that we want to continue to play a part in Erasmus+. Hopefully such participation will encourage our future leaders to believe in collaboration rather than isolation.

Tim Farron is leader of the Liberal Democrats.