Several institutions have objected to the nearly £7 million in special funding paid to the universities of Oxford and Cambridge, some of which helps to cover the cost of applicants' interviews.
Oxford and Cambridge benefit from the Higher Education Funding Council for England's "institution-specific" funding stream, as a contribution to the costs of running their tutorial and interview systems.
No other undergraduate university receives money from this stream; the 17 other institutions to benefit are all small specialists in disciplines including music and drama.
About 13 years ago, Hefce agreed to fund a proportion of the fees charged by Oxbridge colleges, which, prior to the introduction of university tuition fees, were paid by local education authorities on students' behalf.
The Oxbridge funding was originally to be phased out after 10 years, but Hefce agreed to continue it.
Hefce's recent consultation on changes to institution-specific funding brought objections from sections of the sector. "Several institutions ... queried why the universities of Oxford and Cambridge received institution-specific funding, and there were calls for more transparency around this allocation," says Hefce's summary of responses.
All those seeking institution-specific funding must, from 2013-14, make a submission for funding, rather than having the money automatically distributed. However, it is thought that Hefce is unlikely to change the Oxbridge arrangement.
An Oxford spokeswoman said the university "intends to make a case for the continuation of this funding, which in part contributes to the cost of the tutorial system". Cambridge gave the same response.
A Hefce spokesman said that although the original intention had been to phase out the additional funding for Oxford and Cambridge, in continuing it "we recognise the additional costs at these two universities of particular features including small-scale teaching, the tutorial system, and individual interviews."
The allocations for the two universities (£4.2 million for Oxford and £2.7 million for Cambridge in 2012-13) are more than the vast majority of institutions get under the widening participation premium, designed to assist universities with the extra costs of teaching students from disadvantaged backgrounds.
Only five universities will receive more than £2.7 million from the widening participation premium in 2012-13. Other than The Open University, the biggest beneficiaries are Teesside University (£5.2 million) and Staffordshire University (£3.3 million).
Bahram Bekhradnia, director of the Higher Education Policy Institute, called the Oxbridge payments an anachronism. "Tutorial teaching provides no sort of justification - the funding method doesn't look at and fund any other university's pedagogic approach - and if tutorial teaching attracted premium funding others would want to do it," he said.
He added: "To lose this funding would not be a big blow to Oxbridge with their billion-pound budgets, but Hefce know they'd create a political row, and (Oxbridge) would claim that promises they were given when the college fee was removed have been broken."