Universities should be free to charge whatever fees they like to improve the quality of teaching, a report commissioned by John Denham, the universities secretary, has recommended.

The study claims that lifting the £3,145 cap on fees would mean that universities would no longer have to concentrate on meeting government conditions to secure funding and would instead be able to spend more on teaching.

Sir John Chisholm, chairman both of QinetiQ, the defence technology company, and of the Medical Research Council, also attacks the proliferation of “diluted science” in his report, which he warns could damage the economy.

Denham is due to begin a review of tuition fees next year; they could be raised from 2011. Universities such as Oxford and Cambridge believe more money and independence will enable British higher education to compete with the far more lavishly funded institutions in the United States.

The recommendation will anger Labour backbenchers who are determined to block any further increase in fees because, they claim, it will deter students from poor families applying to university. It is likely that publication of the review will be delayed until after the next election.

Chisholm does not spell out how high the fees could rise but studies based on fees paid by overseas students suggest there could be substantial differences, with the most expensive subjects – such as medicine – costing £20,000 a year. Cheaper degrees, such as history and English, could rise to £6,000-£7,000 a year at the top universities, while some degrees at lower-ranked institutions could stay at the same price.

The changes would allow universities to improve teaching and tackle the shortage of rigorously trained science, maths and engineering graduates, according to Chisholm.

He says there are too many graduates in subjects such as information technology, psychology and “science with x” [another subject] – what he calls “diluted science”.

Chisholm says universities are too dependent for government funding on producing research, often on subjects of questionable use, while paying too little attention to teaching.

Sources close to Denham said he shared Chisholm’s concerns that too much funding from government was for research rather than teaching.

Instead, money for research could subsidise the fees of poorer students and provide incentives to study key subjects. “The fixed cap on student fees provides little scope for demand to influence the quality of supply,” said Chisholm.

“Universities are driven by the demands of their government paymasters and student customers.”

Healso recommends changing hitherto sacrosanct features of student life such as short terms and long vacations, as well as making studying more flexible so undergraduates find it easier to do paid work at the same time.

His report comes as confidential data circulated to university vice-chancellors suggest the boom in higher education may finally be stalling.

Figures from the Universities and Colleges Admissions Service (Ucas) show that applications by December 16 were up 0.2% on a year ago. In 2007 applications rose by 7.8%, while in 2006 it was 5.3%.

The latest figures are a snapshot, because not all the applications have yet arrived, but they show falls even at some of the most prestigious institutions – the number of UK and European Union applicants at Bristol is down by 1.6% compared with a year ago.

Others have seen significant rises – those at Exeter, for example, have increased by 23%. At Manchester, applications have gone up 1.7%.

Stephen Williams, the Liberal Democrat universities spokesman, said worries over debt and the value of a degree may be putting off applicants, “particularly at the margins”.

Rob Wilson, his Conservative counterpart, said “the growth in student numbers is depressingly flat” .

Ucas declined to comment in advance of the official statistics being released next year. A spokesman said it was “far too early to draw any conclusions”.

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