Instead, such students should have the option to pay their fees in advance at a discount of 10 per cent or take out mortgage-style bank loans, says the Policy Exchange report, More Fees Please.
Under the scheme, the Government would ensure that banks charged sub-commercial rates of interest so that all students had access to some sort of subsidised loan scheme.
Unlike public student loans, repayment would not be income-dependent. To lower the risk of default and keep interest rates low, the private loans could be secured against major assets, such as parents' houses, the report suggests.
Students from less wealthy backgrounds would not be able to take out the private loans, but would have access to a public loans scheme.
Anna Fazackerley, director of education at the think-tank, said: "Creating a new private loans scheme for these low-risk borrowers would help to reduce the burden of government student loan debt, and target government financial aid at those who need it most."
The think-tank, which has close links to the Conservative Party, also calls on the Government to raise the cap on tuition fees.
"We urge the Government to make its first move on fees a bold one," the report says.
"It is clear that if the cap is set at £5,000 or lower, once again the majority of institutions will charge the maximum fee and no real market will be activated."
In return for higher fees, universities must guarantee investment in teaching and improving the student experience, and must prove they are offering needs-blind admissions, the report adds.
It also calls for a review of the current bursary scheme and highlights the risk that universities will invest more in "merit aid" to reward the brightest students rather than the poorest.
"In an aggressive higher education market where institutions are competing against others in their segment of the sector for the best students, the temptation to push more money into merit-based scholarships and away from needs-based aid will be strong."
As part of a new deal on fees, the Office for Fair Access could require that a proportion of the money universities set aside to support students is directed to need rather than merit. The regulator should be "given teeth", Policy Exchange adds.
The report concludes by attacking universities for waiting for others to make the case for higher fees: "The resounding silence on this subject has done universities no favours."