Some 613,000 people applied to university this year.
Middle class students should be denied loans to cover tuition fees and living costs so that bright poor pupils do not lose out, a think tank says.
The Institute of Public Policy Research says the current system whereby the government funds fees and grants of all students up front is too costly.
The cap on university places means many able pupils are not getting on degree courses, despite rising unemployment.
The government says a review of student finance is due later this year.
The call comes as thousands of A-level students scramble for university places.
At midday on Tuesday about 138,000 would-be students were chasing the remaining 4,200 places left in clearing - the system by which unallocated university places are allotted.
Some 17,800 out of an estimated 22,000 clearing places have already been filled, the university admissions service said.
The shortage of places has been prompted by a cap in places, the growing number of students making the grade for university entrance and a surge in demand - a record 613,000 would-be students have applied for university places this year.
Academics commissioned by the IPPR argue, in their paper "First Choice? Challenges and opportunities for the UK's university sector", that the current system of student finance is an expensive one.
University tuition fees in England are currently limited to £3,225 a year for students starting in 2009-10 and are paid upfront by the government.
These do not have to be paid back until the graduate is earning at least £15,000 a year.
Tuition fee loans cost the government £33 for every £100 borrowed while maintenance grants cost £21 for every £100 borrowed because interest is linked to inflation, the researchers said.
In times of financial hardship it was sensible to direct resources towards the most needy, they said, rather than make them universally available to families on incomes as high as £80,000 and above.
A sliding scale could be introduced dependent on income that could ensure that the poorest benefited, they added.
IPPR researchers also called for better financial support for part-time students and improved use of bursary schemes so that they are targeted towards poorer students rather than simply the brightest.
Former IPPR research fellow Kay Withers, argued that the current financial climate meant tough choices had to be made.
"If the difficult choice in this context means increasing contributions from those who can most afford it - more affluent parents - to ensure that support maybe widened to those who need it, including part-time learners, then this should be done, no matter what the political connotations," she said.
The government is due to begin a review of student finance later this year, which will look at raising the tuition fee cap.
Visiting research fellow at IPPR Mike Kenny said the government should learn its lessons from the "mistakes made this year in allocating university funding, which has resulted in many qualified students not finding places".
He added: "In the short term jobs are harder to get - even for graduates - but as the economy moves out of recession, we will need a more skilled workforce.
"The government should put in place funding to ensure far more young people with good qualifications can afford to go to university and are able to find places in the year's ahead."
He added that many potential students from poor backgrounds were still being put off as a result of the complex system of fees and grants, bursaries and scholarships.
"The current system of financial assistance to poorer students is not fit for purpose," he added.
A spokesman for the Department for Business, Innovation and Skills said: "This government is committed to ensuring that finance is not a barrier to people going to university whatever their background which is why we are spending £5bn on student support this year alone, with about 40% of students receiving a full grant.
"We will be launching an independent review of fees later this year which will which will look at all aspects of student finance and support for students.
"Before we can do this we will publish a framework for excellence in the autumn identifying how we maintain our world class status."