Vice-chancellors have proposed radical steps to address the gulf between surging demand for higher education and the number of places available under government restrictions.
One suggestion is that more than 100,000 extra university places be created with no additional funding, a move that would hit the traditionally sacrosanct "unit of resource".
Another is that British students be given the option of paying international-level fees to secure places, allowing the wealthy to bypass the cap on numbers.
The proposals follow a 23 per cent increase in the number of university applications this year, and come after Lord Mandelson acknowledged last week that "this autumn there are likely to be more disappointed people who do not achieve the university place they aspired to".
David Green, vice-chancellor of the University of Worcester, told Times Higher Education that the sector should accept about half of all qualified but unsuccessful applicants in 2010-11 on an unfunded basis. He predicted that this would result in up to 150,000 students financed by tuition fees alone.
Professor Green said the reduction in teaching funding per student - the unit of resource - would be "the least worse evil".
"It's better to have a slightly diminished student experience than to say to 100 people: 90 of you are in and ten of you have lost out - try again next year," he said.
He suggested the move would help the sector win public support, pointing to the example of California, where higher education funding was slashed by 20 per cent last year.
Professor Green said that in response, the state's universities had "astutely positioned themselves on the side of the would-be student", channelling public disquiet so effectively that Governor Arnold Schwarzenegger proposed a change to the state's Constitution.
Under the amendment tabled last month, the University of California and California State University systems would be guaranteed to receive at least 10 per cent of state revenues.
Professor Green said UK universities could also benefit from "siding with the student".
"We won't win public support by pulling up the drawbridges and arguing that we won't put them down until we have more cash," he said.
However, Les Ebdon, chair of the Million+ group of new universities, said that student support and teaching costs would have to be factored in, and warned that taking on large numbers of unfunded students "would lead to a significant diminution in quality".
Pay your way
The second proposal to address the mismatch between supply and demand comes from Ruth Farwell, chair of the Guild HE group of colleges and specialist institutions.
She said British students should be able to secure places by paying fees normally charged to foreign students, who are unaffected by the cap. At present, she said, "even if you're swimming in money, you cannot buy a place in a publicly funded institution as a private individual".
Professor Farwell, vice-chancellor of Bucks New University, said it made little sense that privately schooled students receive state subsidies once they reach university.
She argued that those who could afford to pay more were taking up limited publicly funded places, leaving some students unable to secure a place and depriving many others of their first choice of course.
Professor Farwell said this "domino effect" could be addressed if students were given the option of paying for places, provided they had the required grades.
"We're not advocating opening up places to those who can pay at the expense of others," she said.
"We want to be sure that publicly funded places go to those most in need."
However, it seems doubtful that these radical proposals will find favour with the Government.
Speaking at the Lord Dearing memorial conference at the University of Nottingham on 11 February, Lord Mandelson warned against large-scale unfunded growth.
Arguing instead for further expansion of "alternatives to university", with a focus on foundation degrees, part-time study and honours courses "delivered intensively" over two years, the peer said that "as tempting as it may seem", it would be a mistake to "guarantee every applicant a full-time place".
The First Secretary said that such an approach made "no sense in terms of the cost to the public purse or the provision of quality teaching".
"A large-scale, untargeted further expansion of full-time three-year degrees without any attention to what these additional students are studying, or how well it equips them for life at work, also makes no sense at a time when we need to be focusing on strategic skills and alternatives to full-time study," he said.