University heads are warning a no-deal Brexit is "one of the biggest threats" the institutions have ever faced.
Higher education leaders have written to MPs to say it is "no exaggeration" to warn that it would take universities "decades to recover".
They say it would undermine scientific research and threaten universities' £21bn contribution to the UK economy.
The government has said its immigration plans will keep universities "open to the talent we need from Europe".
A joint letter from university groups including Universities UK, the Russell Group, Guild HE, Million Plus and University Alliance was sent to all MPs on behalf of the heads of 150 UK universities says: "Vital research links will be compromised, from new cancer treatments to technologies combating climate change. The valuable exchange of students, staff and knowledge would be seriously damaged."
Dame Janet Beer, president of Universities UK, warned that "time is running out".
She says that without "cast-iron assurances" about the UK's access to European research networks, world-leading researchers will be lost to other countries where "funding is not at risk".
But the journalist and educationalist Toby Young, who says he backs a "clean Brexit", dismissed the warning as "the usual ultra-Remainer hysteria", accusing vice-chancellors of "fear-mongering".
"In the event of a no-deal Brexit, I'm sure the government will use some of that £49bn windfall to compensate British universities for any short-term losses," said Mr Young, associate editor of the Spectator magazine.
The Russell Group of leading research universities says there has already been a downturn in EU students wanting to study in the UK.
Data from its 24 universities shows a 3% fall in EU students in the current intake - which they believe is because of uncertainty over Brexit.
The letter warns MPs of the dangers to the UK's universities if they lose their place in European research networks. It gives two examples of funding at risk - the European Research Council and Marie Sklodowska-Curie Actions - which would be worth £1.2bn to UK institutions over the next two years.
University leaders say that in the event of a no-deal Brexit, UK institutions would "immediately become ineligible" for this funding.
After next year, there is a wider pot of European research funding at stake, worth more than £90bn.
Universities want assurances that any lost research funding will be replaced by the UK government.
But they are also worried by proposals for new restrictions on EU students after Brexit in the government's White Paper on migration, published before Christmas.
These 130,000 EU students will need to have visas and be sponsored by universities - and the Russell Group has warned that it is "unrealistic and unsustainable" to expect universities to take on the administrative burden.