Lloyd's has said its offer is final and will be withdrawn if it is accepted by less than 70 per cent of the Names.

''I don't believe that the alternative for members is anything other than a very lengthy, costly and uncertain prospect leading to an ultimate figure little different from that now proposed,'' said Lloyd's chairman David Rowland in an open letter to the Names.

The Names allege fraud, breach of duty and negligence by their agents and advisers who use the investors' pooled wealth to back insurance policies.

Lloyd's has lost GBP5.52 billion in its three most recently reported years.

Names, who pledge all their personal wealth to back insurance written in the Lloyd's market, have had to bear GBP3.13 billion of the losses so far.

The cause of Lloyd's plight stems from the market's trademark unlimited liability policies. In the late 1980s there was a boom in the insurance market, premiums sank so low they barely covered the liabilities, and risk assessment was haphazard as Lloyd'stook in more business in an increasingly competitive environment.

Poor underwriting and inadequate reserving meant the market was unable to ride out the bumps that arose in the form of a string of massive claims for pollution, environmental clean-up costs, and health litigation arising from policies written decades ago, and a series of catastrophes.

That is not to say that Lloyd's was not profitable. According to UBS insurance analyst Chris Hitchings, until 1988 Lloyd's had produced an average pre-tax return of six per cent for the past 40 years, even after costs, including profit commission.

Names do not have to hand over any money to Lloyd's; they merely have to pledge it. In the meantime, they can invest their money and earn income on stocks, bonds and other liquid investments in addition to the profits from the insurance these assets underwrite.

Under the terms of their membership of the venerable market, which means taking on unlimited liability, Names must meet all claims.

But so great are their losses that even if they accept what Lloyd's is offering them Names still owe large sums of money.

Angry and financially crippled, many Names say they expect to get more money in the courts than by accepting the money Lloyd's is offering them, which would repay about 40 per cent of their losses.

''I made one disastrous mistake, so why make another?'' said Fernanda Herford, who backed policies underwritten by the Gooda Walker agency. ''I just can't sign my claim away. Lloyd's isn't outside the law.'' Fifteen years after pledging GBP100,000 to back insurance policies whose premiums were supposed to provide her with comfortable returns, the 50-year-old mother of two owes Lloyd's GBP1.1 million. And she is not alone.

Thirty-eight action groups have sprung up to co-ordinate litigation for Names.

The offer is weighted in favour of four of the heaviest loss-making syndicates, the pools of Names' wealth collected to back specialised lines of insurance. These four syndicates' losses were exacerbated by the London Market Excess (LMX) re-insurance spiral, which multiplied many times over the already substantial hits the Lloyd's market had taken.

Essentially a fee-driven phenomenon, some underwriters took on re-insured liabilities without proper knowledge of the risks they were accepting and then inadequately re-insured these risks, leaving them with substantial exposure.

This pass-the-parcel spiral coincided with a spate of seven catastrophes between 1987 and 1990, costing Lloyd's an estimated GBP13.6 billion.

Based on the votes of the largest action groups, it is most probable Lloyd's settlement will be rejected by the litigating Names.

Names from the Feltrim and Gooda Walker action groups have overwhelmingly rejected the Lloyd's offer. The Feltrim Names were offered 26 per cent of the money in Lloyd's settlement proposal; the Gooda Walker Action Group was offered 24 per cent of the total.

Names participate in more than one syndicate to spread their risks; for some, however, the opposite was the case and every syndicate they were placed on by the agents was loss-making.

The Association of Lloyd's Members, a body representing Names and which has traditionally followed a supportive line for Lloyd's, said last week that straw polls from its 14 meetings held around the country had shown two-thirds of Names would accept the offer. The majority were continuing to underwrite.

Eight out of the 11 association committee members plan to accept the Lloyd's offer.

''The future of the offer is not a foregone conclusion,'' said Neil Shaw, the association's chairman.

With court dates approaching for some action groups, Names are having to weigh up how much they might win and how long it will take for litigation to be settled.

Gooda Walker Names, whose case comes up on April 26, were told by their lawyer that their GBP570 million lawsuit would take two years. Clearly, for some this will be too long.

''It's going to be a war of attrition that will go on and on until Names run out of patience, money or stamina,'' said David Tiplady, a senior partner at the London law firm DJ Freeman, which represents many of the dissident Names.

And the litigation will be expensive. ''We have already paid out more than GBP10 million of legal fees, with the most expensive stage still to come,'' said the steering group for Lloyd's Agents', E & O Line Slips, a body representing the insurers carryingthe agents and advisers' liabilities.

Just as there is no certainty of winning lawsuits, there is also a limited amount of money that will be available from the agents' and advisers' own professional liability insurance, called errors and omissions cover, to pay Names if they win in court.

According to Lloyd's, there is between GBP820 million and GBP1.08 billion in the errors and omissions pot. From this, about GBP400 million is being made available for the settlement.