Universities need to lose their "sense of entitlement", says Charles Clarke, former Labour education secretary.
Mr Clarke says universities can appear ready to take public funding, without doing enough to serve the public interest.
With Edward Byrne, head of King's College London, he has written a book calling for universities to engage more with society's problems and divisions.
They also propose businesses should pay more towards university costs.
"I think there is too much sense of entitlement in universities that says we have a right to be supported by society. But you have to demonstrate your value to society," says Mr Clarke.
The former Labour minister, now aged 69, has gone from being a student leader in the 1970s to education secretary in the 2000s. Now, in his post-political life, he has been working with universities in the UK and the US.
In The University Challenge, co-authored with Professor Byrne, he has put this experience into a manifesto for a modern university - warning that too often they have been inward-looking and resistant to change.
He says high-quality universities are vital to helping with the "grave challenges and opportunities" of social and technological change.
But he does not think they are getting sufficiently involved in addressing the social divisions seen in the Brexit debates and the challenges of "left behind" towns.
Taking the long view, he says universities have changed much less than the society around them, and argues they need to be more ready to innovate.
Mr Clarke's most controversial issue as education secretary was pushing through an increase in tuition fees in 2004 to the then startlingly high level of £3,000.
It was so politically toxic that it caused a bigger backbench rebellion than the Iraq War - almost toppling a Labour majority of more than 160 seats.
The level of tuition fees in England still remains unresolved, with Boris Johnson's government set to respond to Philip Augar's review calling for a cut in fees from £9,250 to £7,500.
Mr Clarke rejects Labour's current policy to scrap fees - and says he was "shocked" to see that leadership candidate Keir Starmer is sticking to abolishing fees.
But he suggests that universities have not really helped their case by all charging the maximum fee level.
"There's a dishonesty that says all universities are the same - a law degree from every university is of the same value - and I don't think that's true," he says.
"I don't think people believe it's true, but universities say it is.
"When we put up the fees to £3,000, I was certain that there would be some recognition that there was a different value for different kinds of degrees and courses. But that never happened," says Mr Clarke.
Mr Clarke says it's important for universities to stay independent from government.
But he says university autonomy "doesn't mean they lose all obligation to serve society", either in terms of how they focus their research or how much they charge their students.
Mr Clarke and Prof Byrne argue that businesses should share more of the cost of higher education.
They propose that employers should pay a levy for graduates on their staff - recognising that businesses benefit from the skills taught in higher education.
Mr Clarke says he is "sceptical" of warnings that such a levy would deter employers from hiring graduates.
He also wants to remove interest charges on student loan repayments and for maintenance loans to be enough to cover living costs.
But he doesn't believe that abolishing tuition fees is a credible plan - saying that governments will always prioritise spending on schools and fees are needed to provide universities with a protected income.
The big challenge for universities, he suggests, is to stay relevant to the problems facing the communities around them.
In a "post-truth" world of populist politics on right and left, Mr Clarke says universities should be advocates for asserting facts and evidence, rather than complaining about how the public debate has changed.
Whether in universities or politics, he suggests that if there are no solutions to "the problems that people were bothered about, it's not surprising that people look to easy sound-bites".
The University Challenge: Changing universities in a changing world. By Edward Byrne and Charles Clarke. Published by Pearson Education.
Sean Coughlan - Education correspondent