Number 10 has refused to deny that some members of the Cabinet have expressed concerns over top-up fees.

The admission came on Thursday when the Cabinet was given a presentation on the issue by education secretary Charles Clarke.

At the end of the 45-minute talk, the prime minister reaffirmed his determination to press on with changes to university funding.

He told the Cabinet he was "convinced" that when people had heard the arguments, they would recognise the merits of the scheme.

This came despite signs that up to 150 Labour backbench MPs could defy the government over the issue.

The official spokesman could not confirm that there was unanimous support from the Cabinet.

"There was support. I've chosen my words," the spokesman told journalists.

Number 10 insisted the government's solution to university funding was the best way forward.

Downing Street said a report from the Council for Industry and Higher Education had underlined the fact that 80 per cent of new jobs until 2010 will require higher education skills.

Ministers were also warned that business would go elsewhere if it thought Britain was not committed to higher education.

"People recognise this does involve difficult choices for government and families," said Number 10.

"We argue that this is a concept that people need time to think their way through. Equally it's an issue which the government believes that while the choices may be difficult they have to be made."

"Do we believe that people should have a right to go to university if they have the ability?"

Later in the Commons the education secretary defended the principle of variable student tuition fees despite criticism from his own MPs.

Speaking at education questions Clarke said top up fees allowing universities to charge up to £3,000 per year were preferable to a flat rate fee being applied across higher education.

Ministers have been criticised for failing to debate other options for increasing university funding.

But answering a question from Bury MP David Chaytor, Clarke said a flat rate fee would not recognise the different benefits degree courses provide.

"Our assessment is that flat fees would be more unfair than a variable fee system," he said.

"Every university would be forced to demand the same amount across the board irrespective of the demand, nature of quality of the course and the potential rate of return for the student.

"That would remove flexibility, it would lead possibly to course closures in institutions which would have no flexibility in deciding what to do, it would lead to lower quality than variability would mean, it would mean we wouldn't have no ability to influence access through the regulator in that way we have set out and finally it would lead to redistribution from poorer to more affluent students."

But the Conservatives said Clarke's answer was an acknowledgement that variable fees would create a supply and demand market which would discourage and price out poorer students from the best courses.

"The secretary of state has claimed that universities which charge a zero fee would encourage students to study there thus admitting that universities which charge a full fee would discourage students from studying there," shadow education secretary Tim Yeo said.

"The government's policy will mean that in the future will be on basis of ability to pay and not on the basis of academic ability."

Clarke responded by arguing that the level of a fee would be only one of many factors driving student choice.

"They will take into account things like the rate of return from different courses, whether they want to study away from home or not and a whole range of different issues of that type," he told MPs.

Liberal Democrat education spokesman Phil Willis questioned how the government would pay for the new scheme.

He raised the question of where the Treasury would find the additional resources needed to pay universities.

"It is inconceivable that some estimate has not been made of the amount the chancellor will sanction - otherwise he will be giving universities a blank cheque," Willis said.

"My fear is that the chancellor will balance what he loans in top-up fees with reductions in grants as has happened since 1998 and the introduction of tuition fees."