This summer there will be 40,000 more unsuccessful university applicants than there were in 2008. This is because we have seen an 8 per cent rise in the number of applications, but institutions won't recruit more students than they did last year for fear of being fined. If restrictions were lifted, universities could admit 10,000-15,000 more students, provided there was additional funding. If some of these places were financed by the Higher Education Funding Council for England, and all received student support for fees and living costs, the bill for each would be about ?10,000 in 2009-10.

There is a simple way to meet these costs. The Government should offer a 20 per cent discount to any 2009 graduate who repays some or all of his or her loan by 31 October. Some 300,000 students will graduate this year, the first generation to pay top-up fees. Most have taken out loans of about ?10,000 to cover fees and up to a further ?15,000 for living costs. We do not yet know the total owed by the Class of 2009, but a conservative estimate puts the figure between ?3 billion and ?4 billion. If ?125 million (or 5 per cent) of this were repaid with a 20 per cent discount, it would yield enough cash to fund 10,000 extra students. This would cost the Treasury little or nothing.

When the loan scheme was introduced, ministers argued that the public-spending cost of a student loan was "only" the costs of the interest-rate subsidy and those loans that weren't repaid. If a loan is repaid over, say, 15 years, the subsidy alone is more than 20 per cent. The period of subsidy will be longer now because fewer graduates will find well-paid jobs this summer. But if it bought out loans with a discount, the Government would avoid the subsidy - and generate cash now, which is its prime concern.

It might be argued that some graduates would repay their loans without discounts, so the Government would lose 20 per cent of what would have been repaid anyway. To some extent this is true and might look like an extra subsidy for the middle classes, although actually it just replaces the subsidy they already get from the subsidised interest rate.

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Past patterns of repayment are based on lower levels of debt, so we do not know how many loans might be repaid without a discount. And if the Government were worried about missing out, it could limit the scheme to the fee element of loans and test the hypothesis by seeing how many students also repaid the rest of what they owed. It would then have evidence to support future schemes to incentivise repayments. Alternatively, it could offer the discount only to lower-income students, information the Student Loans Company already has.

So an enlightened Government could enable graduates to repay loans to help them through a difficult start to their careers, allow several thousand more students to attend university and raise much-needed cash for the Treasury. This sounds like win-win politics to me.

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John Craven, Vice-chancellor, University of Portsmouth

Chair, University Alliance.