Someone shopping around for comprehensive annual cover can now expect to pay £585.84, according to the AA's British Insurance Premium Index.
The cost has surged by 16.3% over the past 12 months, adding nearly £82 to a typical motor policy. A year ago, a motorist shopping around for a deal could expect to pay around £503.90.
The continued "epidemic" of whiplash claims has helped to push up the cost of cover, as have two recent hikes in insurance premium tax (IPT), according to the report.
The AA estimates the recent IPT increases have added around £18 to the average car insurance premium over the past year - and it urged the Government not to impose any further hikes in this tax in the Autumn Statement.
"We are witnessing sustained price increases once again which is bad news for drivers," said Michael Lloyd, the AA's director of insurance.
He continued: "I can't see an immediate end to the current upward trend."
Mr Lloyd said: "The whiplash epidemic has dogged the British motor insurance industry for a decade and continues to do so.
"Drivers are still being pressured into making claims for often minor collisions they might have forgotten about. This is pushing up claims costs, because insurers can't prove that an injury wasn't suffered."
He said the activities of claims management firms make life more difficult for those with a genuine injury.
Looking across the UK, motorists in Northern Ireland appear to be the worst hit by price hikes in the past three months, the index found.
The average premium for a motorist in Northern Ireland who shops around has risen by 11% over the past quarter to reach £861.79.
Scotland remains the cheapest part of the UK to insure your car, with average premiums there costing £422.10 for someone who shops around.
Looking across different age groups, 60- to 69-year-olds have seen the biggest jump over the past three months in the premium they were offered, with a 5.4% increase. But people in this age group still pay the lowest average premiums, at £361.04.
Young drivers aged 17 to 22 saw their average premiums increase by 3.6% over the quarter to £1,286.96. They pay the biggest premiums out of all the age groups.
The AA's index calculates the average of the five cheapest quotes that someone who shops around for insurance would be offered.