The Association of British Insurers (ABI) has carried out its second benchmark survey of motor insurer compliance with the ABI claims code.
Results show customer satisfaction remains high.
The survey of more than 6,000 claimants showed 85% were satisfied with how their insurers had handled their claims, and 89% said they were handled efficiently.
But not all the results were positive. Roughly 60% of those who made complaints felt their complaints were not handled fairly.
The ABI said insurers had been working to improve this area over the last six months by revising complaints procedures and investing in staff training.
ABI motor manager Jo Dagustun said: "How well an insurer performs when a claim is made is the key test for any policyholder.
"This latest survey shows a consistently high level of customer satisfaction with insurers' overall claims handling performance, but also points out a few specific areas for improvement.
"It is evident that insurers are seeking to address these areas of concern."