Half of motorists think it should be unlawful for insurers to charge existing customers more than new customers for the same cover.
That finding has come from research by Go Compare Car Insurance, which also found that 61% of drivers think new customers get a better deal on their insurance than do those renewing their cover.
Go Compare said motorists could save up to £247.29 by shopping around for car insurance rather than simply renewing with their existing provider.
It said that while many businesses reward customers for loyalty, insurers tend to do the reverse by charging them higher premiums than those for new customers.
Despite the savings it said were on offer, some 62% of motorists allowed their car insurance to automatically renew, Go Compare found.
It said the Financial Conduct Authority (FCA) had sought to force insurers to improve renewal information to help customers make a better-informed decision about their cover and its cost.
As a result, since 2017, renewal letters must now remind customers they can compare prices and levels of cover offered by alternative providers and be alerted to the possibility of a better price elsewhere at the fourth or subsequent renewal. But Go Compare found only 46% of drivers remembered seeing last year's premium alongside their renewal price.
Only one-third said the previous year's premium was clearly shown on their renewal documents and 29% remembered being advised to check the cover level, while only 22% recalled the 'shopping around' message.
Last year, the CMA recommended 'naming and shaming' insurers who overcharge loyal customers and using targeted price caps to protect vulnerable customers.
Lee Griffin, a founder of Go Compare, said: "Car insurance is a market where dual pricing has existed for a long time and where comparison sites have made the practice far more transparent for people who can often see exactly how much their current insurer is discounting for new customers.
"There's absolutely no good reason why insurers should be able to do this - other than they've been able to get away with it. Loyal customers have every right to feel ripped-off."
