A survey of more than 1,000 parents reveals that almost half (48.6 per cent) believe the proposed hike is unfair because it will impact mainly on the less well-off, while a further three in 10 (30.3 per cent) believe it is unfair on everyone.
Just a fifth (21 per cent) think increasing fees is necessary given the current economic climate.
The survey, conducted by parenting website Netmums, reveals that many parents believe higher fees will leave them unable to help their children with the cost of university – while others say they will have to start saving now.
Under the proposals, recently approved by Government, English universities will be able to charge students up to 6,000 per year in fees from 2012, and as much as 9,000 in "exceptional circumstances".
But almost a third (32.2 per cent) of the parents polled said they no longer expected to be able to afford to help pay their child's fees, which means they will be unlikely to be able to go to university.
A further 18 per cent said they were unlikely to be able to help fund the cost of the fees, but were happy that their child could apply for a Government loan.
More than one in 10 (11.3 per cent) said they no longer wanted their child to go to university due to the fees rise and the debt they would leave with.
A third (32.7 per cent) of those questioned said they planned to start saving now to help their child go to university in the future.
The online survey questioned 1,100 parents in December.