This compared with about a fifth of male undergraduates, the YouGov survey of 1,061 students found.
Overall, some 27% of the students said they had a mental health problem. This rose to 45% among lesbian, gay, bisexual and transgender students.
Universities UK said institutions were working hard to develop good services that linked in with the NHS.
Of those students who said they had a mental health problem:
- 77% had depression
- 74% had anxiety
In May, statistics published by the ONS showed student suicides had risen to their highest level since numbers were first recorded in 2007.
These figures - for 2014 - showed there were 130 suicides in England and Wales among full-time students aged 18 or above. Of those, 97 deaths were for male students and 33 were females.
There has been concern about the level of mental health support services provided by universities.
But the survey showed students were broadly aware of the mental health services offered by their universities.
Some 18% of students had already made contact with university mental health services, and, of those who had, nearly nine out of 10 had seen a counsellor.
Of those surveyed, 30% of males and 27% of females said they would not feel comfortable in talking about their mental illness with friends or family.
Chief executive of Universities UK Nicola Dandridge said universities took student mental health "very seriously".
"For some students, an unfamiliar higher education environment can be stressful, particularly for those who already have an underlying illness.
"Some students are reluctant to disclose their difficulties, which can also present a challenge for universities seeking to support them."
But she added that the development of policies and anti-stigma campaigns was beginning to address these issues.
"The challenge for universities is to build on the support services and external links that exist already, enabling referral to the NHS where necessary," she said.
"It is important to remember that university wellbeing services, however excellent, cannot replace the specialised care that the NHS provides for students with mental illnesses."
Universities UK also said it had issued guidance to all universities last year with advice on dealing with students with mental health issues.