More than 120 rebel Names have accepted or expressed an interest in accepting a final settlement offer from Lloyd's. Those that do not agree to the deal will face debt enforcers.
In the 1970s and 1980s, a series of mainly asbestos-related claims led to market losses of £8.1bn. As a result, thousands of private investors, called Names, were left in the red.
In 1996, more than 700 Names worldwide, owing a total of £300m, turned down a deal with Lloyd's to settle. But earlier this year, Lloyd's made them a final offer to write off some of the debt.
Now around one in seven have either accepted the proposal or asked for their cases to be referred to an independent panel to assess their financial status.
Adrian Beeby, spokesman for Lloyd's, said: “We think that this is an extremely positive response. We are pleased to see so many Names have listened to us saying that this is our final and best offer.
“We hope that they take independent advice and know this is the right time to settle.
“Should they choose not to accept, we will have no alternative but to resort to debt enforcement measures.”
Chris Stockwell, adviser to the United Names Organisation (UNO), said out of the association's 200 members, one has accepted and 40 have expressed an interest in doing a deal based along those lines.
“The suggestion that Lloyd's is going to get any money from this process is laughable,” said Stockwell. “Lloyd's is trying to use intimidating tactics. The courts will not allow it to bankrupt people when there is still an appeal hearing outstanding and other issues remain to be heard.”