Universities have been accused of running a "cartel" and failing to offer enough two-year bachelor's degrees, by a right of centre think tank.
The UK 2020 report argues that fast-track degrees could cut student debt.
It is backed by Labour's Lord Adonis and Sir Anthony Seldon, vice-chancellor of the University of Buckingham, which offers two-year degrees.
But the umbrella group Universities UK said uptake of existing two-year courses had been limited.
And a spokesman pointed out that official investigations have previously found that competition in the sector was largely working well.
"Several universities have been offering two-year, fast-track degrees for a number of years, but the demand from students has been limited under the current fees and loans system in England," said UUK in a statement.
Plans to boost two-year degrees were announced by Universities Minister Jo Johnson in February.
The UK 2020 report, co-authored by businessman and Leave.EU co-funder Richard Tice, says fast-track degrees could cut student debt, enhance choice and relieve pressured housing stocks.
It argues that tuition fees, reaching £9,250 this year, have failed to deliver real choice or competition for students in England and describes mounting student anger about debt and interest rates as a "timebomb" beneath the system.
It says most universities charge the maximum fees allowed and have acted as a cartel to slow reforms and freeze out private sector competition.
"Price competition is the area where most notoriously the universities have failed to deliver," says the report.
"In the long term, smarter ways of funding students will have to be found."
The authors argue that students promised a better experience by the increase in tuition fees were "sold a lie", while vice-chancellors with massive pay packets are the biggest beneficiaries.
The report estimates that two-year degrees could reduce individual graduate debt by up to £20,000, with major savings in accommodation costs.
Mr Tice said complaints of poor value for money from friends who were parents of university students prompted him to write the report.
"Investigating the truth behind these stories has shocked me, the powerful university cartel, interwoven with parts of the establishment care lots about money and little about students."
Lord Adonis, in a joint foreword with Conservative MP and UK 2020 chairman Owen Paterson, said: "It is not often that politicians from such different parts of the spectrum come together on a major question of such national importance.
"But we are united in our desire to find a solution to the crisis in how students and universities are funded."
Sir Anthony said the report did "an excellent service in channelling the debate on higher education towards the contemporary structure and its antiquated provision".
In its statement, Universities UK said it expected three-year undergraduate degrees to remain the preferred option for many students.
"But if changes can be made to the funding and fees system in England that help increase the flexibility of provision and are in the interest of students, this is a good thing."
Chris Husbands, vice-chancellor of Sheffield Hallam University, added: "Two-year degrees may make financial sense for some students.
"However, due to the compressed nature of a two-year degree there would be a significant reduction in opportunities for students to do part-time and vacation work which many students from lower or average income households rely on to help fund their university life.
"It is also less likely that a student would have the opportunity to carry out work placements or work-based learning in their chosen subject or area of study.
"This means their skills and readiness for the workplace could suffer as part of a two-year degree.
"The real need is for a funding regime which encourages more part-time study and study alongside work."