The study by a management consulting firm predicts further cuts in public funding to universities. Some 60 senior university leaders from across the UK responded to the survey, around a third of the total.
"It is clear that we are witnessing a sea-change in the dynamics of higher education", said co-author Mike Boxall.
Declining government grants, limits on undergraduate numbers, higher student fees and cuts to research funding have resulted in a dramatic shift in priorities for university leaders, argues the report by PA Consulting.
The report notes that the past year has seen a "marked softening and increased discrimination" in demand for higher education from school-leavers in response to higher fees and patchy graduate employment prospects.
Demographic changes and visa restrictions on international students also limit the pool of would-be students.
Some 58% of the university leaders surveyed said they were worried by falling demand for undergraduate courses from UK and EU-based students.
Some 90% expressed concerns over declining numbers of postgraduate students from the UK and EU, with more than 80% worried by falling international numbers.
Source: BBC News