As a growing minority in Lloyd's begin to think the unthinkable, Ted Benfield, a broker with Kininmonth Lambert, believes a blanket refusal to pay is the best way forward.
"I've been thinking of contacting Names to get them to repudiate their liabilities," he said. The resultant legal quagmire could take years to sort out.
Mr Benfield's view is supported by lawyers on both sides of the Atlantic. A corporate Lloyd's rising from the ashes would be able to write new business in the United States with little difficulty.
Jonathan Bank, a partner and insurance expert at Chadbourne & Parke's LA law office, argues that a worldwide shortage of capacity would force US insurers to turn to London for reinsurance. "The regulators would be scrupulous but I don't see them saying you can't deal with a new Lloyd's plc," he said.
A new company would have the advantage that it would not be burdened with the old liabilities for asbestosis and industrial pollution that brought the present institution to its knees.
Once it gets European permission, it would also be able to offer its backers limited liability, sharply increasing the attraction of being a Name.
Lloyd's, however, dismisses suggestions that a Lloyd's plc could arise to replace the existing market. "The DTI would have to relicense Lloyd's as a plc," said a spokesman. "And there's no way they would allow a phoenix Lloyd's."
One British lawyer pointed out that the Government would not want to be seen bailing out wealthy Names, or American lawyers, who profit most from asbestosis and pollution suits.
The possibility of a Lloyd's meltdown grew stronger at the weekend as Names examined the rescue package proposed by David Rowland, its chairman. Key to the plan is the establishment of Equitas to reinsure old syndicates - groups of Names.
The deal calls for pounds 2.8bn to be raised - the lion's share from investors in old syndicates, and only a tiny fraction from underwriters, brokers and future Names.
The cash would in part be used to fund Equitas. But if the reinsurance company didn't have enough capital to pay claimants, the liability would return to the Names. If, on the other hand, it ended up with a surplus, there is no guarantee the cash would be returned to the investors.