Science and research should be a priority in the talks between the UK and the EU, says the Russell Group of research intensive universities.
Any barriers "would be bad for the UK and bad for Europe", said the group's acting director, Tim Bradshaw.
His comments come as the EU prepares to authorise the start of the talks.
The EU's chief negotiator, Michel Barnier, is due later on Monday to seek a formal mandate from the European Council in Brussels to begin negotiations.
Mr Barnier expects the talks to begin immediately after June's general election.
The Russell Group says there will be "no winners" if Brexit results in barriers between researchers and has pledged to work with "all sides to secure a positive outcome".
Dr Bradshaw said there had been "huge breakthroughs in medicine, engineering, and any number of fields" as a result of joint working, which he promised would continue after Brexit.
"We want to maintain the closest possible relationships with colleagues across the EU, and research must be a priority during talks," he added.
He called for the rights of EU students and staff at UK universities to be guaranteed after Brexit.
"We value our EU colleagues very highly and need urgent assurances, that after Brexit, they will retain the same rights to stay and work in the UK that they have now.
"Nearly half of all UK academic articles result from international collaboration and EU member states are some of our biggest partners.
"These relationships improve the quality of UK research and underpin the strength of our science base."
UK universities are among the biggest beneficiaries of the EU's huge Horizon 2020 research fund.
Non-EU countries can also draw on the fund if they contribute to it - but a major condition of countries being able to participate is allowing freedom of movement for researchers, a potential stumbling block in the talks.
The Conservative party manifesto, promises to "collaborate in science and innovation" with EU member states.
The manifesto also pledges to secure the entitlements of EU nationals in Britain and British nationals in the EU.
"There may be specific European programmes in which we might want to participate and if so, it will be reasonable that we make a contribution," the document adds.
Labour's manifesto promises that the party in government would "ensure that the UK maintains our leading research role by seeking to stay part of Horizon 2020 and its successor programmes and by welcoming research staff to the UK".
The party also says it will seek to maintain membership, or equivalent, with European organisations that offer benefits to the UK such as Euratom and the European Medicines Agency.
The Liberal Democrat manifesto warns that "the Leave vote has already started to affect existing and proposed research programmes".
"We will campaign against any reduction in investment in UK universities and for their right to apply for EU funds on equal terms."
Manifestos have not yet been published for the SNP, UKIP or the Green Party.

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The 35-year-old striker received his 'Guldbollen' - Golden Ball - award on Monday at a ceremony in Stockholm.
The statue will go outside Stockholm's Friends Arena, where Ibrahimovic scored four goals against England in 2012.
Ibrahimovic said: "It's huge for me. Most people do not get a statue until they have passed away."
The Swede has won the award every year since 2007 - and also came top in 2005 before losing out to Arsenal midfielder Freddie Ljungberg a year later.
Ibrahimovic retired from international football after Euro 2016. He scored 62 goals in 116 games for Sweden and has won the domestic league title in four different countries.
"After all the hard work for 15 years in the national team - and 20 in my club career - it feels like it is appreciated," added Ibrahimovic, who joined United in the summer from French champions Paris St-Germain.
"The guy from Rosengard [a district of Malmo where the majority of residents come from an immigrant background] will get his own statue in the capital. A big thank you to everyone."
Swedish Football Association president Karl-Erik Nilsson said: "The statue is a way for us to thank Ibrahimovic for his amazing efforts for Swedish football, but it is also a symbol for everyone to always be reminded and inspired by all he has done."
Barriers to research collaboration in Europe as a result of Brexit would harm scientific progress, says a group of leading UK universities.
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Manchester United's Zlatan Ibrahimovic will have a statue erected in his honour after being named Sweden's top player for a 10th successive year.