More than half of students would be willing to pay university fees of £5,000 and one in five would be prepared to go as high as £10,000, a survey of tens of thousands of students suggests.
Opinionpanel Research asked 37,000 university students what price would be so low that it would make them doubt the quality of their courses, and what figure would be so high that they would rule out paying it.
More students were prepared to pay fees of £3,000 - approximately the current level - than any other sum.
But a report on the findings by Anna Vignoles, professor of economics of education at the Institute of Education, says the results also indicate that "a reasonable number" would be willing to pay higher fees, with demand remaining "substantial" even at £7,000.
Unsurprisingly, poorer students would be less willing to pay more.
For example, if fees were £6,000, 44 per cent of students from fee-paying schools say they would not be willing to pay to study the courses they were taking, compared with 54 per cent of students from state schools.
"If fees are raised, it will be important to ensure that poorer students have sufficient financial assistance so as not to deter them from entering higher education, or limiting their choices to the lowest-cost universities," says the study, How Much More Will Students Pay?
Social background was less of a factor than other variables examined. The most important driver of how much students were willing to pay for a degree was the subject of study.
If tuition fees were increased to £6,000, about 60 per cent of education students would refuse to pay, compared with less than 40 per cent of medical and dentistry students.
"This suggests that students' expectations of how much their degree will 'add value' to their earning potential has a greater impact on the willingness to pay than does their social background," the report says.
It concludes that "there is a case for the introduction of variable tuition fees within each institution".
There were also significant differences in students' answers by type of university, even when respondents were from the same background or studying the same subject.
For example, Russell Group students who attended fee-paying schools were significantly more willing to pay £4,000 or more than their University Alliance peers.
The study suggests that overall, if tuition fees were increased to £5,000, 65 per cent of students at Russell Group universities would be willing to pay, compared with 60 per cent at 1994 Group institutions and 52 per cent at Alliance universities and the Million+ group of new institutions.
Almost half (47 per cent) of Russell Group students would be prepared to pay £7,000, compared with 38 per cent of Million+ students.
In addition, almost a third (30 per cent) of Russell Group students say they would pay as much as £10,000, as would per cent of those at 1994 Group universities, 24 per cent of Million+ students and 23 per cent of Alliance students.
Professor Vignoles said the findings suggested that the optimum model would be for institutions to charge different fees for different subjects, but also for universities to be "mindful of where they position themselves in the market".
Female students were significantly more likely to reject higher tuition fees than male students, while those with lower entry grades were also less prepared to pay more.
Students from some ethnic groups were less open to the idea of paying more than others, even when they hailed from the same socio-economic background.
Responding to the findings, Wes Streeting, president of the National Union of Students, said: "This report is valuable evidence of how genuinely variable fees would cause serious negative effects.
"It is clear that students from disadvantaged backgrounds, women and those from some ethnic minorities would be priced out of elite universities, pushed away from the subjects they really want to do, or forced to make the calculation that higher education simply isn't for them."
The report is based on data gathered from members of Opinionpanel's student panel who were surveyed during their first term at university between 2006 and 2009.