Universities will have to bid for a quarter of places
Universities in England will have to compete against each other and private providers for a quarter of their student places.
Universities Minister David Willetts has published plans to increase market forces in higher education in England.
Promising to put "students in the driving seat", he also announced there would be 20,000 places reserved for degrees with fees of less than £7,500.
Labour's Gareth Thomas said the plans meant a "race to the bottom".
The shadow universities minister told MPs that this was a "desperate drive to cut fees, no matter what the cost to quality".
In the higher education White Paper, a controversial plan to create extra places for privately-funded individuals has also resurfaced - on the basis that it will be restricted to those sponsored by a business or a charity.
There are also proposals to allow students to repay their loans early, although the government is still consulting on the detail.
This is a politically sensitive suggestion which raises the prospect of better-off students not paying as much as those who pay back their loans over several decades.
Mr Willetts said the reform package would "open up the system" and "put power where it belongs - in the hands of students".
The White Paper, called Students at the Heart of the System, details plans to make universities bid for a proportion of their places - a higher proportion than had been anticipated.
This raises the prospect that while some universities will expand, others will lose student places.
Mr Willetts said that no government could offer a guarantee that courses or even institutions might not close as a result.
This proportion of universities bidding for places is "just the start", said Mr Willetts. "We want to extend the system so more places are contestable."
From 2012, universities will be able to offer unlimited places for students achieving AAB grades at A-level or better - regardless of the total student quotas they have been allocated.
This will encourage top universities to compete for the 65,000 students each year who attain these grades.
There will also be 20,000 places allocated on the basis of "good quality" and "value for money" at institutions charging an average of £7,500 or less per year.
Since a high proportion of universities have announced fees above this level, these places could be taken by an expanded private sector or courses provided through further education colleges.
Sir Steve Smith, president of the vice-chancellors' body Universities UK, warned that this "must not undermine the quality of the higher education system".
In terms of improving social mobility, there had been discussion of changing the admissions system to allow applications after students knew their exam results - which previous official reports had recommended as fairer.
But a decision on this - so-called "post qualification application" - will not be considered until a review reports back next year.
The White Paper also promises to reduce barriers to private providers entering higher education.
This includes a review of the use of the term "university" as a title.
And there will be an emphasis on improving the information available to students.
Last week the Higher Education Funding Council for England (HEFCE) announced that universities would have to publish key information about courses, such as the average salary of former students, the cost of accommodation, teaching hours and satisfaction ratings from previous students.
There will also be plans for inspections to be triggered if there are concerns about the quality of courses or teaching standards.
But students were unimpressed.
Aaron Porter, president of the National Union of Students said: "Fees have been tripled and students have been exposed to the potential chaos of the market and yet there are still no concrete proposals for how quality, accountability and access will be improved."
Lecturers also attacked the proposals as an attempt by the government to recover from having lost control of fee levels.
"Trying to force down the cost of a degree after the government got its sums wrong will not solve the funding crisis it created," said Sally Hunt, leader of the University and College Union.
Professor Les Ebdon, chair of university think-tank Million+ said there was no evidence that competition would improve the student experience.
"A mini-market in 'AAB' students could favour students from independent schools and actually constrain a university's ability to widen access," he said.
Dr Wendy Piatt, of the Russell Group of leading universities, said she agreed that universities with high demand for courses from highly-qualified students should be allowed to expand.
But she warned that "such a very selective" lifting of the places cap could make it harder for some universities to maintain teaching in strategically important subjects like sciences and languages.
Professor Paul Welling, of the 1994 group of research intensive universities, said the government needed to avoid driving down standards by auctioning students to low cost institutions.
"We should not encourage higher education providers to short change students by cutting corners."
Competition on price will not affect Scottish students in Scotland's universities where there are no tuition fees. In Wales there are plans for Welsh students at Welsh universities to receive a subsidy covering increased tuition fees.
A decision on tuition fees and support for students at Northern Ireland's universities is expected in the autumn.