A third of parents who help with their children's car insurance believe high premiums will force them to give up these payments after European gender equality rules come into force a month from today.
From December 21, insurers can no longer consider a customer's gender when calculating what their insurance premium or retirement income should be, following a ruling by the European Court of Justice last year.
More than six out of 10 parents surveyed by insurer Aviva believe the new rules will push up the cost of car insurance for their children, while just 8% believe premiums will drop.
Some 32% of parents surveyed who contribute to their child's insurance costs predicted that premiums will go up by such an extent that they will have to stop paying for their child's car insurance.
However, Aviva said these views may be premature, with industry predictions that premiums are likely to fall by up to 10% for young male drivers while increasing by up to a quarter for young women.
A person's sex has traditionally been taken into account when assessing insurance risk, with women typically benefiting from smaller car insurance premiums due to their lower accident rates.
Aviva found that there is still a large amount of confusion over the implications of the new gender rules, with only one in five parents saying they are confident about what the changes will mean.
Comparison website MoneySupermarket said it is yet to see car insurance providers applying vast pricing changes.
It said that early indications show the hikes are not as sharp as anticipated and are around 2% so far.
Clare Francis, consumer finance expert at MoneySupermarket.com, said: "For car insurance, consumers need to consider the full picture, and for that they need to think about all the details that affect the cost of cover.
"A raft of other factors, from postcode to profession and points on a licence, will influence the cost of insurance.
"Don't take the drastic step of cancelling cover and applying for a new policy now - you may incur a hefty cancellation fee in the process."
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Aviva's research also found that a third of parents plan to swap their child's car for a less expensive model and nearly half (44%) said they will have to consider increasing the contributions towards their children's premiums to keep them on the roads.
The insurer said younger drivers can help to cut insurance costs by using telematics technology which rewards careful drivers with lower premiums, consider using a less powerful car and try to park off the road and in a garage.
More than 1,000 parents who pay for their child's car insurance took part in the UK-wide Aviva study.
