Tuition fees will have to rise to at least £6,000 a year to cover teaching costs, a survey of England's university managers suggests.
Parents now contribute £4,000 per year to support students
The Guardian poll of 100 university heads reveals growing unease about the new funding system which allows a maximum £3,000 fee to be charged.
It is also suggested that fees for some science courses could reach £10,000.
Many vice-chancellors also thought the Treasury would make student loans more expensive to cover unpaid debts.
The government is now writing off around £1bn a year in unpaid debts, the newspaper notes.
A questionnaire was sent to every university in England, almost all of which charge the maximum fee for courses.
Some 40 vice-chancellors responded - most anonymously.
Vice-chancellors from the Russell Group - the top 20 universities which conduct the most research - said maximum fees of £3,000 would have to at least double following a review of the system in 2009.
One Russell Group head suggested families should expect to save much more for their children's education.
However, he told The Guardian: "No university would risk losing their top students by overpricing.
"If the cap were to be lifted to say £5,000, that would become the new universal fee. It would not be variable."
Another vice-chancellor said there was a direct link between the resources available for teaching and the quality of graduates produced.
Comparing the average funds available to teach an undergraduate in England, £7,300, with those available in the United States - some £11,500, he said there were only two ways to bridge the gap.
"One is by increased government grant, which seems unlikely in the present circumstances, the other is by a higher tuition fee charge," he added.
Higher Education Minister Bill Rammell said fees were fixed until 2010.
"Before we get to that point an independent commission reporting to Parliament will report on the first three years' experience of the system and will consider future arrangements for the fee cap and student support."
The National Union of Students said the survey revealed the need for a wider open debate about higher education funding.
The survey comes as student debts are reported to be rising.
A recent report said undergraduates were now paying £13,000 a year in fees and maintenance costs and that they needed more advice to ensure they could manage their finances.