Students would want any extra income generated by their fees to be used to reduce class and lecture sizes, according to the Higher Education Policy Institute survey. Nearly a third of the 15,000 students who responded see this as the top priority.
Students' other priority is the improvement of academic facilities, the survey found. More than a quarter (26 per cent) of respondents want universities to provide better library, laboratory or specialist academic facilities.
Students are more concerned about teaching quality than quantity or the general environment, the Hepi report says.
We asked tutors what they thought.
* Loughborough University tries to keep seminars to 18 students at most, but numbers can go up to 24, according to Brian Jarvis, senior lecturer in American literature and chair of the English department's learning and teaching committee.
"We have a commitment to keep class sizes below that in the first year. If groups reach 24, we get a little anxious because it becomes increasingly unmanageable. Seminars give students a chance to develop communication skills."
If it is simply a question of getting information across, then the size of the lecture should not matter, but the "logistics are at breaking point", he said.
"It's pretty much the same story all over. It's difficult to maintain this commitment with the numbers coming in and no more money for staff.
"If students are saying they want smaller class sizes and staff are saying we need more people to teach, then something needs to be done."
Teaching well is all about "horses for courses", according to Andrew Ireland, National Teaching Fellow and subject leader for TV production at Bournemouth University.
About 65 students a year are taught using a mixture of interactive lectures, seminar groups of 15 students for debating ideas, workshop groups of eight to ten students to learn how to use camera equipment and editing suites, and groups of six students for production and filming activities.
"It's not about teaching contact, it's about facilitating their learning.
We have to set them up to enable them to learn in their own time, in groups and independently. There's pressure to reduce teaching contact but at the same time enhance the student experience."
The way the course is run allows staff time for research and enterprise work and for one-to-one tutorials for final-year students.
"You can't use seminar groups for everything. Sometimes you need to have big groups to provide certain information, otherwise you would end up repeating content more times to smaller groups," Dr Ireland said.