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About 12 universities are looking into reducing their 2012 fees in the wake of policy changes.

Ministers now say 20,000 student places will be held back for universities charging less than £7,500 fees.

This was seen by some as a way to reduce fees, after many universities opted for the £9,000 maximum.

The Office of Fair Access (Offa), which monitors university access for poorer students, said the universities had sought information on cutting fees.

Under the new tuition fees regime, universities wanting to charge fees of more than £6,000 have to negotiate an "access agreement" with Offa on measures they will take to recruit students from disadvantaged backgrounds.

In its White Paper, published in late June, the government detailed plans to take back 20,000 student places from across the university system.

Institutions with average annual tuition fees of less than £7,500 will then be able to bid for these places.

But this was after many institutions had announced their fees for 2012.

On Thursday, Offa said that "about 12" universities had since approached it seeking details of how to renegotiate their access agreements in order to lower their fees.

The body said most of those were already charging average fees - which take into account fee waivers - of a little more than £7,500.

Professor Eric Thomas, the incoming president of the vice-chancellors' body Universities UK, said changing fee levels would be a "complicated calculation", and that universities would need to move fast if they intended to do so.

He also warned the government "not to further accelerate the pace of change".

Prof Thomas was addressing the body's annual conference after a year which has seen, in England, tuition fees raised to up to £9,000; teaching budgets heavily cut; and the White Paper, which outlined a more market-based system.

He said universities were concerned about plans to create a market in England for top students.

The White Paper included plans to allow universities to accept as many students as they can attract with AAB grades at A-level or higher.

There are fears this will lead universities to focus particularly on competing for these high-achieving students, and on offering cheaper-to-run arts courses which often have higher entry requirements than science ones.

"We are anxious that deregulation by academic achievement will have consequences for social mobility, student choice and for the sustainability of some Stem [science, technology, engineering and maths] courses," Professor Thomas said.

Business Secretary Vince Cable, who also addressed the conference, said the plan would give students a better chance of getting a place on the course of their choice.

He said that the increased fees, due to come into force in 2012, had led to "inevitable uncertainty" over student demand, amid speculation that potential students would be put off.

But he said he was "cautiously optimistic", and that vice-chancellors had been reporting "encouraging numbers" of prospective applicants at open days.

On Wednesday, Alan Milburn, a former Labour cabinet minister who has been appointed to advise the government on social mobility, urged more action to encourage disadvantaged students to enter top universities.

He called for more use of information about a student's background in offering university places.

Currently some universities take into account whether an applicant is from a high- or low-achieving school, and accept pupils with lower grades if they come from more challenging backgrounds.

Mr Milburn said he believed vice chancellors wanted to make more use of this approach, but were fearful of "media hostility".

"Universities have to summon up the courage to get out and make a positive argument for change," he said.

"It cannot be done surreptitiously. It has to be done openly."

The White Paper applies only to England, but changes are taking place elsewhere in the UK.

In Scotland, home students do not pay tuition fees but the Scottish government has said that from 2012, universities will be able to charge up to £9,000 for students from the other UK nations.

The Welsh Assembly has announced that fees will rise to up to £9,000, as in England, but the government will meet the extra cost to Welsh students studying at any UK university. Funding for universities in Wales has been cut by 12%.

Ministers in Northern Ireland have said that 2012 tuition fee levels will remain close to 2011 prices, but not yet given full details.