The Office of Fair Trading's (OFT) report into liability insurance has sparked calls for the resurrection of the Department for Work and Pension's (DWP) employers' liability pilot project.
AXA, Royal & SunAlliance (R&SA), Allianz Cornhill, Zurich and the ABI have told Insurance Times they would like to see the study return.
The pilot, aimed at speeding up the claims process, was shelved earlier this year when the TUC withdrew support because it felt members of the legal profession would be unfairly represented.
The ABI said it would like to see a relaunch of the scheme, if necessary without TUC support.
AXA head of liability claims and professional services Matthew Scott said: "We will be looking to the OFT report to get things going again."
A DWP spokesman said it would discuss matters with all stakeholders. "We hope to make an announcement once these talks have concluded" .
Last week the OFT's report ruled out a further investigation into the liability market. It found that overall rises in liability premiums had been lower than in previous years.
But it warned lower premium increases should "not give way to complacency", and called for continued communication within the sector.
It also said the after-the-event market would be subject to further reviews by the DWP and Civil Justice Council.