A hardcore rump of rebel Names have defiantly rejected Lloyd's final offer to settle the ongoing dispute over the liability of asbestos claims.

Approximately a third of the 200-strong United Names Organisation (UNO) voted to reject the offer in a recent meeting. But another third said they were undecided and the final third said they would seek further information about the terms of the deal.

Chris Stockwell, head of the Lloyd's Names Association, said there was not “a hope in hell” of some rebel Names agreeing to Lloyd's final settlement offer. The deadline to accept the offer is February 26.

In January, Lloyd's offered to write off some of the £300m debt owed by the Names who refused its reconstruction and renewal package in 1996, brokered after the market suffered huge asbestosis claims.

A group of rebel Names refused the offer, claiming the market knew about the losses before asking them to invest.

Stockwell said: “People feel they have ignored the Jaffrey ruling, which called the Names innocent victims of a staggering catalogue of incompetence and failure. They are incensed by the offer.”

A show of hands at the meeting revealed a third of UNO Names are not even going to apply for more information, and just one third intend to “see what is on offer”.

The warnings come in light of the revelation that Richard Carter, one of the Names, approached Mr Justice Cresswell, asking to end his membership with UNO so he could continue litigation independently.

UNO members cannot settle with Lloyd's without the organisation's permission.

Adrian Beeby, media relations manager of Lloyd's, said: “Lloyd's position is that it hopes that anyone who wishes to take advantage of the settlement offer will be free to do so, and we hope that UNO will view this issue constructively and positively.

“With respect to the recent UNO meeting, we were not present but are surprised by the negative view since Lloyd's has received many positive communications from Names worldwide and has been very encouraged by the approaches.

“This underlines the fact that it is a very generous offer, and it is giving the Names an opportunity to consider their own personal position and circumstances and take advantage of getting rid of this litigation once and for all.”