The average price quoted for comprehensive car insurance had dropped by over 2% in the last three months, revealed the AA's British Insurance Premium Index.
It said this drop was the largest since January 1996.
The cost of non-comprehensive cover had also fallen over the same period, but by less than 1%, said the AA.
AA Insurance director Neale Phillips said the last quarter's figures pointed to some large players in the market launching a price war to gain market share.
But he warned that it was too early to draw any conclusions.
“This is not the first time we have seen dramatic premium falls,” he said.
“Soon after the AA Index was launched, insurance premiums fell sharply but the market was quite different then. Low premiums couldn't be sustained and some insurers exited the market while others consolidated, quickly leading to rising premiums.
The AA Insurance Premium Index has celebrated its 10th anniversary of tracking car and home insurance prices.
“It's been a dramatic decade,” said Phillips. “What the next ten years will bring is hard to say, but motorists are more likely to be hit by costs such as tolls, congestion charging, fuel prices and parking than by rising insurance premiums.”
