Although some members said the new proposals did not go far enough, leaders of the main action groups fighting Lloyd's made clear they thought it would probably be enough to persuade members to vote in favour during the summer. But many still plan to press for more help for the hardest hit.
David Rowland, chairman of Lloyd's, said the settlement was the only practicable route forward. "By making these changes we believe some of the less palatable areas have been made more acceptable to members and a lot of people will find their situation greatly improved."
Michael Deeny, chairman of the largest action group, Gooda Walker, and of the litigating names' committee and a member of Lloyd's ruling council, said: "It's for the names to decide on the offer but these are substantial improvements and there can be no doubt that it significantly increases the chance of it succeeding."
The Association of Lloyd's Members (ALM), the biggest names representative body with 9,000 members, welcomed the offer, but also called for pensions for elderly names who have been ruined by Lloyd's.
John Mays, chairman of the Merrett names association, said "My view is that the cost is coming down and the contributions are going up and it has a much better chance of flying. "
However, Christopher Stockwell, chairman of the Lloyd's Names Association Working Party, said: "This is nothing like enough. We do not regard this as final and we are keeping on with our campaign."
Alan Porter, chairman of the Devonshire Names' Action Group, said the pounds 300m increase in the settlement fund was "meagre and disappointing" and he called for further aid for ruined names. He also warned that "Lloyd's troubles over fraud and breaking of regulations in the US may cause the collapse of the settlement."
In California, a court cleared the way for renewed legal actions by the state against the market, which are expected to have the backing of the US Securities and Exchange Commission. But in a separate Tennessee decision Lloyd's reached an agreement that allows it to continue negotiations with names.
The market's offer to names has been raised by pounds 300m to pounds 3.1bn as a result of extra contributions of pounds 100m from brokers, an agreement by auditors to pay more than pounds 100m, an increase in the proceeds from selling and mortgaging Lloyd's property and other contributions from central resources.
As revealed earlier this week, Lloyd's has also reduced the cost to names of setting up the Equitas reinsurance vehicle that is to take over their old liabilities from pounds 1.9bn to pounds 1bn.
In a letter from Mr Rowland, Lloyd's said there would be more help for the "honourables" - names on lossmaking syndicates who have paid up - and extra assistance for names who cannot pay at all.
An important part of the settlement is a reduction in the cap set on names' future liability for further losses. In the earlier proposal, 9,000 names were to be capped at pounds 100,000 maximum. Now all but 2,000 of these will be capped at lower levels.
Those who remain members are to have their cap reduced to zero. Those who have paid but left will see it reduced to pounds 50,000. And for those who cannot pay and who have very large losses, there will also be a reduction in the pounds 100,000 cap.
Lloyd's said the number of names who will receive cash refunds as a result of the settlement has doubled from 5,000 to 10,000. These are people who have paid their debts in full.
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