Paul Marshall, executive director of the 1994 Group of small research-intensive universities, said there was a risk that "interest will soon be lost in British education".
Speaking at the International Partnerships in Higher Education conference in London last week, Mr Marshall said: "We already invest less in our universities than other OECD countries and find ourselves passed by our competitors.
"With dramatic cuts and changes to the visa system coming in...Britain must not be seen as shutting itself off to the rest of the world with hostile attitudes."
Fabrice Hénard, higher education analyst at the Organisation for Economic Cooperation and Development, said that the key factors influencing international students were the language of instruction, tuition-fee policy and immigration strategy.
Mr Marshall argued that universities should take responsibility for the continued promotion of a positive message about UK higher education: "This must be a story shared unequivocally by institutions and government."
He added: "What we urgently need to realise is that when we institute new policies, these changes will affect our position in the global higher education market."
Mr Marshall also presented figures from the Quality Assurance Agency that reveal the breadth of UK universities' involvement overseas.
In Malaysia, for example, 72 UK institutions have more than 200 links with 107 university partners. One UK university is working with 19 different partner institutions in the country.
But Christine Ennew, pro vice-chancellor for internationalisation at the University of Nottingham, predicted that this trend for multiple partnerships could come to an end.
"Rather than have relationships with 20 institutions in a particular country, we might expect to be focusing on a smaller number of key strategic partners," she said.