Rebel Names have refused to accept Lloyd's final offer to settle.
Last month, Lloyd's unofficially offered to write off up to two-thirds of the £300m debt owed by the 700 Names who turned down its reconstruction and renewal package in 1996.
Lloyd's put its final proposal in writing last week, offering to accept between 30% and 35% of outstanding liabilities.
But the United Names Organisation, the main UK pressure group and funders of the Jaffray case, has reacted strongly against the deal.
Co-chairman Catherine Mackenzie Smith said: “This ‘offer' is a demand, not an offer. It shows the incompetence, arrogance, and malevolence that has characterised Lloyd's dealings with its Names.
“Names cannot afford this crazy demand; most will have no choice but to continue to litigate for justice.”
Lloyd's spokesman Adrian Beeby said: “These comments are deeply unhelpful. We believe this is an extremely generous offer and represents the best last chance the Names will have to settle their liabilities.”
Mr Justice Cresswell, who had requested that Lloyd's took steps to settle, described the ongoing legal wrangle between the two sides as “the biggest piece of civil litigation this court has seen”.