A quarter of a million new undergraduate places will be needed by 2010 if English universities are to keep pace with predicted levels of demand from students.
Demand has already begun rising
Depending on what government does about this, people might not get the places they want.
The Higher Education Policy Institute says the demand will come from a combination of population growth and more students staying on to take A-levels.
A paper by the think tank's senior researcher Libby Aston says demand rose little during the 1990s but has gone up by about 10,000 places in each of the past two years.
Future demand is "extremely difficult to predict", especially as the impact of the recent changes to A-levels - with the introduction of AS-levels and Vocational A-levels - is not known yet.
But the projected increase in the population of young people will almost certainly result in demand for about 150,000 additional undergraduate places.
There are currently about 1.33 million undergraduates in England.
That is without any increase in the participation rate - the proportion of young people wanting higher education.
Ms Aston says the A-level reforms are likely to be the key to that. If targets for attainment in schools are met, the proportion of 18-year-olds with two or more A-level passes is likely to rise from the present 40% to 46% by 2010.
This would imply an additional 100,000 higher education students - making an overall total, she estimates, of between 180,000 and 250,000 extra places, possibly more.
In addition, postgraduate numbers might rise by 40,000 to 50,000.
If the rise in undergraduate numbers is at the higher end of the prediction, the government would be close to its aim of having 50% of young people experiencing higher education.
The assumption in the government's white paper on the future of higher education is that the bulk of the expansion will be in the newly-introduced foundation degrees.
The omens are not good, given that there has been a decline in demand for existing sub-degree qualifications - HNDs and HNCs - of about 5.3% since 1997.
"So far, it is not clear that there is major demand for this type of degree and this type of qualification either from students or employers."
If they were clearly defined in consultation with employers to meet regional skill needs, and promoted well, the new foundation degrees could be "very successful".
But Ms Aston cautions that in the past, government targets have had a limited impact on the total number of students and the type of courses they wanted to pursue.
The director of the institute, Bahram Bekhradnia, said: "It will be a tough assignment for the government to put most of the growth into foundation degrees.
"The worrying thing is that they actually decided not to provide any additional student numbers in 2004 and 2005. This is a very surprising decision given the very strong demand.
"There is a possibility, if the government does not increase first degree places, that young people will come out of school wanting to do a degree and
finding they're not available."
The Department for Education and Skills said all the numbers in the report looked "speculative".
Foundation degrees had found support from both private and public sector employers.
"Future funding for student places will be dependent upon future spending reviews but we will of course take account of how student demand is growing and changing," a spokesperson said.
BBC education correspondent Mike Baker says the predictions in the report would mean problems for all political parties.
As things stand, there is no funding for any extra places for next year.
He says politicians must either find considerable extra funding through taxation or higher student fees, or risk the anger of thousands of students unable to get a university place.