More than 600 rebel Names have turned down Lloyd's final offer to settle the long-running battle over liability for asbestos claims, causing the 300-year-old market to waive the deadline.

Lloyd's had offered to write off some of the £300m debt owed by the 700 Names who turned down its reconstruction and renewal deal in 1996.

But fewer than 100 Names have accepted the financial package, leaving more than 600 willing to carry on the legal battle.

Of these, 170 of the 200-strong United Names Organisations (UNO) have also refused the settlement proposal because of confidentiality issues. Husbands and wives of Names are worried that their financial details would have to be disclosed.

Only 23 members of the UNO have contacted Lloyd's in writing to accept the offer.

The “final” deadline, which has already been pushed back once on February 26, was supposed to end last week on March 12. It now appears to have been quietly dropped.

Adrian Beeby, media relations manager of Lloyd's, claims that out of the 700 Names offered the proposal, a “huge figure” has contacted Lloyd's.

“Our position is still unclear,” he said. “Quite a number have indicated their willingness verbally, so we have to be quite flexible with the deadline.”

The market was struck by £8.1bn of mainly asbestos-related losses in the early 90s, which gave rise to accusations that underwriters knew these long-tail losses were in the pipeline, but kept them hidden from Names.

A group of Names, that did not accept the 1996 Reconstruction & Renewal offer, has been unsuccessfully fighting Lloyd's in the courts.

Catherine Mackenzie Smith, co-chairman of UNO, said: “One of the most common reasons why it was turned down is that people do not trust Lloyd's.

“They don't want to tell them all their business as they are not satisfied with confidentiality levels.

“A lot of people's spouses have also refused to co-operate and give their financial details.”

She added many of the Names would not be able to afford to accept the offer, as 62 have already been forced to sell their houses.

They are now threatening to continue their battle in the courts.

“It is a shame really,” Mackenzie Smith said. “But it is really a case of much too little, much too late.”