About 300,000 new places will be needed at universities over the next 12 years, experts predict, making the higher education funding model unsustainable.
A rise in the number of 18-year-olds by 2030 will push demand up by 50,000, the Higher Education Policy Institute says.
A further 350,000 places will be needed to keep pace with the existing growing participation rate, it adds, but other factors may reduce that by 50,000.
The government has set up a review of university fees and funding.
Last year, 534,000 students were accepted on to the hundreds of mainly three-year degree courses on offer in England.
The Hepi report examines the impact of policy changes on university entrant rates, feeding a number of scenarios into the calculations to arrive at the 300,000 figure.
The 18-year-old population has been declining steadily for a number of years, but from 2020 it will increase again, rising by nearly 23% by 2030, says Hepi.
Questions for future
It estimates there will be 14,709 additional entrants arising from demography alone, which will amount to about 50,000 additional students by 2030.
And if participation continues to increase at the current rate, about 350,000 extra places will be needed on top.
Countervailing factors such as Brexit, are likely to reduce that total by about 50,000, the research says.
Currently, more women than men go to university.
And if males were to increase their rates of participation, the research says, 500,000 extra places would be needed in total by 2030.
It notes that there is not much sign of a change ahead in this area but cautions that the higher education system would come under great pressure and require a comprehensive reassessment if there was.
Bahram Bekhradnia, one of the authors and Hepi president, said as nearly every new student required a government-subsidised loan, "it is difficult to see - under the current finance model - how the policy of uncapped student recruitment can continue".
"This is particularly pertinent given the constraints on public expenditure and the absence of any suggestion from the Treasury that more money will be available for higher education in the future," he added.
The report says the policy consequences of this very likely large increase in demand need to be considered.
"Given the extent of the loan subsidy provided for student loans... the higher education budget will need to be significantly increased in order to meet the financial consequences," it says.
They suggest a cap on student numbers may have to be reintroduced.
A DfE spokesperson said: there were more people going to university than ever before - including record numbers of 18-year olds from disadvantaged backgrounds entering full-time.
"We want anyone with the talent and potential to have the opportunity to go to university, which is why we lifted the cap on student numbers and reduced barriers that people face.
"We are conducting a major review of post-18 education to ensure that the system provides genuine choice for young people, and students and taxpayers are getting value for money."