In total, only ten responses were received from UK universities after the education think-tank, the Higher Education Policy Institute, asked a number of higher education institutions to divulge a breakdown of their spending information.

The think-tank wanted universities to follow the example set by Texas State University in the United States, which publishes an itemised breakdown of its costs, and plans to publish a pamphlet containing the data.

Nick Hillman, director of HEPI and former advisor to ex-Universities Minister David Willetts, said: “I’d like to see our universities adopting an approach similar to the local authorities on how they spend their council taxes, where they itemise spending on individual services.”

He insists that without a clearer understanding of the way universities spend their money, it will be difficult for them to convince the government to raise the £9,000-a-year cap on fees, introduced by the coalition government in 2012.

Universities “are in a weaker position than they think they are,” he said. Oxford and Cambridge, institutions that both charge the current £9,000 maximum tuition fee, have claimed that each undergraduate student actually costs them around £16,000 per year.

Tuition fees are not the only source of university income, however. The Higher Education Funding Council for England (HEFCE) issued universities with teaching grants of £2,860 per student in 2013/14. This would leave an estimated shortfall of £4,140 per student in 2013/14, if the £16,000 figure is accurate.

However, a spokesman for the University of Cambridge has made the following comment: “The University’s calculations show that there is a £7,600 per year per student shortfall between the cost of undergraduate education at Cambridge and income from tuition fees.

“This shortfall is currently met by the University. The figure was calculated using methodology set down by the Government. All this information has been shared with Mr Hillman.”

In October, Hillman expressed frustration about the £16,000 number in The Guardian. “No one ever explains how figures like £16,000 are calculated,” he said. “Those who use such figures resemble schoolchildren answering their maths homework with a single number and no underlying workings.”

Hillman has suggested that “One reason why higher education institutions are reluctant to produce detailed numbers on their costs is that it would expose internal cross-subsidies”.

In other words, publishing an itemised breakdown of costs would make explicit the ways in which fees from students who study subjects in areas such as the arts and humanities, which are cheaper to teach, subsidise more expensive courses such as medicine and the sciences.

A recent survey published by student finance website Student Money Saver found that 81 per cent of students believe they are overpaying for their tuition, although it did not distinguish between the kinds of subjects the students were studying. Second-year Trinity historian Harry Stockwell agrees: “If universities expect students to believe that £9,000 represents a fair deal for students, they need to be prepared to divulge this information,” he said.