The review has been prompted by a series of court actions in the UK and US over Lloyd's pounds 8bn-plus of losses since 1987, which have already bankrupted thousands of names - wealthy investors who have backed the 300-year-old market.
The continental firms have also lost heavily from their involvement, and several smaller operators are already bankrupt after huge catastrophe losses.
A private co-ordinating body, the International Association for Asbestos and Pollution (Intap), has been set up, led by Cologne Re to look at dealings with Lloyd's.
Intap is due to meet in mid-February, market sources say, to consider voiding cover on syndicates managed by former Lloyd's deputy chairman Stephen Merrett, who was found guilty of fraud last October.
But future moves could be far wider, affecting billions of pounds of business with Lloyd's.
"It would be a very serious matter for people if reinsurers withdrew their cover on a broader front," said the head of a leading names action group.
The survival plan, announced last May, aims to place old liabilities into a new body, Equitas, in return for an intended one-off payment by names.
Further details, which include a pounds 2.8bn settlement to halt lawsuits, are due at the end of February.
Lloyd's faces a wave of fraud probes in US states, and top officials have been served with writs by former underwriter John Donner that allege a cover-up of asbestos pollution problems in the 1980s.
UK names have won negligence claims against Lloyd's agents totalling more than pounds 1bn.
A separate case involving the French re-insurer Axa Re, which is contesting "excess of loss" liabilities on the notorious Gooda Walker syndicates, is due to be heard in the House of Lords in March.Reuse content