The Court of Appeal's ruling in the Jaffray case is expected to be made available to lawyers, on an embargoed basis, on Wednesday, 10 July 2002.
The formal judgment will be handed down about a week to ten days after.
Michael Freeman, a partner at Grower Freeman Solicitors, which represents some of the Names involved in the case, said there had been no hint as to the outcome of the case.
"Having been battered by the legal system for some 11 years, through three different Court of Appeal hearings and no less than nine courts of first instance, I'm afraid my clients are never going to be optimistic until they actually read the result themselves," he said.
The Jaffray case began in 1997 when Sir William Jaffray alleged that Lloyd's downplayed the potential scale of asbestos liabilities to attract Names and their capital to the market. Lloyd's won the original case in November 2000. The case went to the Court of Appeal in March this year.
One barrister with an involvement in the case said: "People are waiting breathlessly for the outcome...It's very much make or break for some people."
Another senior Names representative said: "I personally would expect the Names to lose. The Court of Appeal may express sympathy for them and may criticise Lloyd's, but I find it hard to believe they'll win and that the Court of Appeal will say Lloyd's collectively committed fraud and is entitled to compensation."