Fresh talks between underwriters and agents to thrash out a new settlement are said to be imminent after names - the investors whose assets fund the market - won two court victories last week.
But speculation about such talks comes as Lloyd's Quarterly Trends Survey, published today, reports that underwriters are growing less confident about future growth.
Although most market professionals expect rates and premium income to increase, the proportion expecting an improvement has sunk to the lowest level since September 1991.
Yesterday, a Lloyd's spokesman said he knew of no 'meetings that could lead to a settlement offer'. However, he admitted that Lloyd's always expected that as more expensive actions come to court there would be more of an appetite among names and market professionals to get around the table.
In February, names rejected pounds 900m in compensation, and the offer was withdrawn.
Agents have insisted that there was no more money available, though names have argued that more could come from reinsurers.
Last Wednesday, Michael Sword- Daniels successfully sued his members' agent, H G Poland, to recover losses that already exceed pounds 500,000 and threaten to reach pounds 1m.
And in a separate judgment the Law Lords ruled that members' agents, who put names on to syndicates run by the managing agents, are liable if those syndicates are managed negliently.
Mr Sword-Daniels told the Independent yesterday that he had heard rumours that if he won his case the agents would have to make a revised offer rather than defend the many costly legal actions being brought by names, whose losses in the past three years are about pounds 5bn.
The judge ruled that all his losses should be borne by H G Poland, the members' agent now known as KMR Services, because the firm had a duty of care to ensure Mr Sword-Daniels was not put on the riskier syndicates.
There has been talk that any new compensation could reach pounds 1.5bn, but Mr Sword-Daniels said even that would be inadequate as it was unlikely to indemnify names against future losses. 'We still have the full effect of Lockerbie to come through yet,' he said.
Next week names on Gooda Walker syndicates, who have lost more than pounds 1bn, begin their case for compensation against managing agents.
Members' agents will now also be liable. Last week the Serious Fraud Office abandoned its inquiry into Gooda Walker, something which has raised agents' hopes.
Lloyd's trends survey showed that rates have increased in most marine and aviation areas of business while other areas have seen little change. But in areas of business such as reinsurance and motors they have fallen and are expected to fall further. Competitive pressures, particularly in motor insurance, are behind the downward pressure on rates, Lloyd's said.
David Rowland, chairman, said: 'After the very large premium increases of the past two years, it is not surprising to note a weakening in some areas . . . .expectations over the next three months suggest that there will be further downward pressures in some areas.'
The survey gives a more accurate picture of what is happening in the insurance market because coverage has been extended from 25 panels of underwriters to 79. Market costs are continuing to be squeezed although a slight slowdown is expected over the next quarter.Reuse content