“The exam question for a new PM, a new government, is about Britain’s place in the world, Dan Shah, assistant director of policy at the UK HE International Unit, told representatives from the 139 university-strong membership association at the event in Liverpool.

“It’s important that we’re [universities] not seen as elites, as entitled, but that we are seen to be essential to that job,” Shah said.

“The exam question for a new PM is about Britain’s place in the world… it’s important that we’re seen to be essential to that job”

The impact of the referendum result is already being felt at some institutions. Adrian Dutch, director of international at the University of Westminster, said the university has already received calls from EU students due to enrol this year saying they are not coming or deferring entry due to the uncertain climate.

He voiced a worry shared by many stakeholders at the event, that press coverage of racist incidents taking place in the UK in the weeks since the referendum may also deter EU students.

But the consequences of Brexit could be more far-reaching than Europe, argued Richard Shaw, head of education at Grant Thornton accounting firm.

“Whatever impact Brexit has on EU students, the bigger fear is it will be a PR disaster for UK higher education,” he said, suggesting this could deter international students worldwide, not just from Europe.

With the sector coming under increasing scrutiny, Shah pointed to transnational education as an area where the UK must bolster its reputation, ensuring educators deliver the same quality of teaching as at home.

“I think that’s a huge strength in terms of the resilience of our recruitment from places where it’s a high proportion like China, like Malaysia, but it’s also something that we as a sector may be judged on,” he said.

And as well as positioning the UK on the global stage, there is much work to be done at home.

“The key thing we need to do is start thinking about how we might react to where policy might go,” Shah said, suggesting the sector looks to its counterparts in Europe for good examples.

Universities UK is assembling a team that will work to put forward policy to protect UK HE, he said.

Speaking on Friday afternoon as ongoing cabinet appointments were being announced, Shah urged: “We may not control how fast the cabinet may change, or who may be in there, but we as a sector can think about what our return is: how do we respond to it, what can we give back?”

Andrew Mandebura, head of BUILA’s lobbying team and director of international development at Huddersfield University, noted that a focus on immigration remains for many people a “much more palatable policy than the economic one”, and so universities face an uphill battle to convince the public and government of the financial contributions of international students.

“It’s not enough to show benefit of international students. Instead, paint a picture of what Theresa May’s success would look like”

However, Dutch at the University of Westminster argued that “it’s not enough to show the benefit of international students”, given that immigration restrictions on students have toughened in spite of lobbying from the sector in the past.

“Instead, paint a picture of what Theresa May’s success [in her goal to reduce net migration] would look like,” he urged. “Courses will close. Universities may close.”

Action is all the more urgent given increasing competition to recruit international students from other study destinations, he said, noting: “If the US starts to take international recruitment seriously, it has the capacity to blow not just UK but Europe out of the water.”

And if the UK does see a decline in incoming EU students, he said, “That’s a massive hole that might have to be replaced with students who come from outside the EU, and are therefore more expensive [to recruit].”

Universities must work collaboratively to gather the “hard data” necessary to make a strong case not only to the wider public but also to their own financial directors, he urged.

He pointed to new data produced by Grant Thornton, whose report on the financial health of the UK HE, Adapting to Change, showed the £4bn in overseas student tuition fees amounted to 12% of universities’ overall income in 2015.

“I would be pushing and pushing for people like Grant Thornton to either produce papers or include in their papers information for finance directors on the increased cost factors of recruiting international students,” commented Dutch.