Mr Justice Creswell has reserved judgment until October in the Lloyd's of London versus Jaffray case.
Lawyers completed their closing statements last week at the London Commercial Court, a division of the high court. A spokesman for Lloyd's said judgment is expected in late October at the earliest.
The action was brought by Sir William Jaffray and 220 former names.
They allege senior Lloyd's council members concealed the true extent of the market's asbestos losses in the 1980s.
Lloyd's has pursued the 220 former names for their share of outstanding premiums, totalling £51m, for Equitas, the reinsurance vehicle for pre-1992 syndicate losses.