Private colleges may be allowed to drastically increase their enrolment of students in receipt of public loans if they agree to underwrite the cost to the taxpayer.

Under a little-known loophole, a relatively large number of private providers can already access student loans without facing a cap on their numbers.

Times ÖйúAƬ understands that the government will be forced to close the loophole as it struggles to keep a lid on the cost of the public loans system.

But at the same time, ministers are seeking ways to create more competition for students to keep down tuition fees across the whole sector.

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One solution would be to allow private providers to bid for places set aside under the "core and margin" model mooted by David Willetts, the universities and science minister, in a speech last month.

Under the model, the majority of university places (the "core") would be centrally allocated, with a small proportion (the "margin") distributed via a competitive process.

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The problem is that the "margin" is likely to consist initially of a small number of places, a point confirmed by Sir Alan Langlands, chief executive of the ÖйúAƬ Funding Council for England.

He said last week that a high percentage of contestable places in the "early stages" of the new system would be "destabilising".

Instead, the government may consider loosening the numbers cap for providers if an agreement can be reached over covering the loss to the taxpayer of the student loans.

This could see private providers effectively underwriting the loans by estimating what proportion of fees would be written off and paying this sum up front.

Private providers might be attracted by such a model, especially institutions that charge relatively low fees and are confident that graduates will earn enough to pay off the loans in full.

One ÖйúAƬ sector leader, speaking anonymously, said that private providers would take a "serious look" at the idea, although another said institutions would see it as a "tax".

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Nick Barr, professor of public economics at the London School of Economics, said that such a system could be attractive, but only for low-cost subjects with high graduate returns.

"Such a proposal would not work for, say, a music conservatoire, but it would work for a business school. It is an instrument that could be very useful but for a limited range of subjects," he said.

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He added that the idea had elements of the system that the government should be moving towards for all universities, in order for it to be able to expand student numbers in an affordable way.

Professor Barr and Neil Shephard, professor of economics at the University of Oxford, have proposed that institutions pay an "insurance premium" specifically related to graduate earnings if they decide to charge fees above ?7,000.

This would be coupled with a separate "national cohort risk premium", in which money paid by higher-earning graduates generally would be used to subsidise maintenance loans and fees up to ?7,000.

A sector-wide levy to cover the cost of higher fees was proposed by the Browne Review. But Professor Barr said that relying on such a blanket system alone would create incentives for universities producing low-earning graduates to set fees too high.

The need to tackle the issue was illustrated last week in figures from the House of Commons Library released by shadow universities minister Gareth Thomas.

They showed that student loans would cost the government ?250 million a year more than planned if average fees were ?8,000, which is just ?500 higher than the ?7,500 figure assumed by the Treasury in the government's modelling.

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simon.baker@tsleducation.com.