A number of insurance companies have appealed against the decision to allow pleural plaques sufferers to make compensation claims, public liability insurance holders have been told.
Last week, a judge rejected a bid to invalidate an asbestos related section of The Damages Act which was brought in last year.
The law overruled a previous House of Lords decision which stated that damages could not be claimed for pleural plaques, as it was not classed as a disease and has no symptoms.
Nick Starling, director of general insurance and health for the Association of British Insurers, said that following investigations and legal advice, its members believe there are grounds for appeal.
"Insurers have not taken this decision lightly and it reflects their strong view that The Damages Act is fundamentally flawed, as it ignores overwhelming medical evidence that plaques are symptomless and the well-established legal principle that compensation is payable only when there are physical symptoms," he added.
Kim Baniells, founder of York's Asbestos Support Group, told the York Press that hundreds of people in the region have been affected by pleural plaques thanks to widespread exposure to asbestos dust.