The government is under increasing pressure to revise a decision made by the House of Lords to refuse sufferers of pleural plaques the right to obtain compensation.
Recently, hundreds of union activists lobbied Westminster, urging the Labour administration to overturn the decision.
A form of scarring of the outer lining of the lung, pleural plaques is an indication of previous exposure to asbestos and does not generally cause symptoms.
It is, however, associated with an increased risk of developing diseases such as asbestosis and mesothelioma.
Alan Ritchie, general secretary of the Union of Construction, Allied Trades and Technicians, said pleural plaques victims must receive compensation.
He added: "The Law Lords' decision was a disgrace; the government must have the courage to reverse the decision and reinstate the right of those suffering to receive compensation."
Meanwhile, Unite's deputy leader Graham Goddard added that the decision made by in the House of Lords had been a "disaster for working people".