Lloyd's has offered to write off up to two-thirds of the £300m debt it is owed by 700 Names who refused to accept its 1996 reconstruction and renewal package.
The offer was made at the high court this week, as Mr Justice Cresswell reviewed the costs from the Jaffray case, which Lloyd's won last month. This threw out allegations that Lloyd's covered up from Names the market's £8bn spiral of asbestos claims in the 1980s.
By accepting the deal, under which Lloyd's said it would forego up to 65% of the 700 Names' outstanding liabilities, the Names will have to renounce any right to further legal action.
The 220 Names party to the Jaffray action will each pay £25,000 to settle the cost of that case.
Around 700 Names worldwide will each receive details of the offer in January, together with an individual settlement figure.
Bankrupts are exempted from the deal, as are Names living in Canada because they are subject to a separate settlement offer.
But several bankrupts have asked Lloyd's if they can also be included in the settlement deal
Names will have one month to consider the offer. Debt recovery action will be taken against those who reject it.
Those Names who have difficulty meeting their liabilities will have their case reviewed by an independent panel formed by Lloyd's.
Lloyd's said it hoped that as many of the non-accepting Names as possible accepted its final offer.