The universities minister, David Willetts, has refused to withdraw his claim that most universities will charge more than £6,000 a year only in exceptional circumstances, as cabinet ministers privately admitted the plans were in serious disarray.

Ministers are now looking at cutting student numbers to offset the higher than expected cost of loans to the Treasury from a higher average fee.

Willetts insisted it was too early to say whether most universities would charge the maximum £9,000 tuition fees, but admitted that the Office of Fair Access (Offa) had no power to stop them doing so. He said it was not an overall price regulator in higher education.

Privately, ministers admit they have become the victim of the so-called Giffen good, an economic theory in which people paradoxically consume more as the price rises, violating the normal laws of supply and demand.

Under the theory, the supplier charges more on the basis that people buy more of the product, even as its price rises. [See footnote]

The source admitted that most self-respecting universities were charging well above the £6,000, fearing that, if they did not do so, they would be regarded as second-rate institutions.

Willetts denied it was yet clear that the average level of fees would rise above the predicted annual average, £7,500, claiming that it was too early to say. He also urged analysts to look behind the headline figure and see the lower fees being charged for poorer students.

He said he did not recognise claims that the government would face an extra £1bn bill if universities did charge fees closer to £9,000.

Under the reforms, universities in England will be able to charge £6,000 for undergraduate courses from 2012, and up to £9,000 in "exceptional cases".

Offa, now seeking extra staffing from the government in the face of an unexpectedly high workload, will have to look at the access arrangements of those that charge more than £6,000.

At the weekend, the vice-chancellor of Liverpool John Moores said universities would struggle to keep fees down to £6,000, as ministers want, in normal circumstances.

Speaking on the BBC Politics Show, he claimed the government had got its sums wrong. "We're in pretty lean form as a university and yet the calculation we do is: if we charge £6,000, we'll lose £26m. We can't do it."

Asked if this meant no university could charge the government's preferred £6,000, he replied: "If they do, I don't think they'll be around for very long, and they'll be a very different institution in a few years' time with that under-investment."

With the intentions of 24 universities declared, the vast majority intend to charge fees of £9,000 for their undergraduate degree courses, including universities outside the elite Russell Group. It is expected that at least 60 will charge the maximum. The government modelled its plans for university funding on an estimate that universities would charge fees of £7,500 on average.

Figures released by the shadow universities minister, Gareth Thomas, reveal that, if fees average £8,000, further cuts of £430m will be required over the spending review period. This is equivalent to cutting student numbers by 17,000 a year, 47,000 in total (5% of student places).

The final average fee will be influenced by the number of students offered fee waivers under proposed access agreements, which all institutions planning to charge above £6,000 must submit to Offa by 19 April.

It has emerged that the proportion of students who want to work in the public sector has risen despite the government's swingeing programme of job cuts and plans to limit the sector's much-envied final salary pension schemes.

Female students are particularly keen, according to a major new survey conducted in association with the Guardian, with more than 34% indicating that they most want to land a job in the public sector after graduating.

The Guardian UK300 survey of the country's most popular graduate recruiters – to be formally unveiled on Monday 4 April – reveals that 29% of all students want to work in the public sector, an increase of 0.3% since 2010 and 5.8% since 2009.

The next most popular career category is scientific research and development, with 19.5%, followed by media and advertising (19.2%).

• This footnote was added 11 May 2011. While the term Giffen good arose in this interview, some readers pointed out that the intended reference was probably Veblen's theory. A Guardian blog went on to discuss the distinction.