Names are hoping an European Commission probe into how the Treasury supervised Lloyd's in the 1980s could win them compensation from the government.
Officials for the EC are demanding answers from the Treasury over its supervision of the market when it was facing mounting losses from £4bn of asbestos claims.
The probe was initially launched late last year after the EC received up to 30 separate complaints from former Names at Lloyd's.
Chris Stockwell, chairman of the Lloyd's Names' Association, said: "The inquiry focuses on the way the DTI co-operated with Lloyd's in amending certain auditing requirements so that auditors no longer had to certify the liabilities of individual Names but instead rely on information from managing agents."
The inquiry was believed to have been winding down following a flurry of letters between the EU and UK government in February.
But last week the commission fired another salvo to the government, in the form of a 12-page questionnaire, after the completion of the Jaffray case.
Although, Lloyd's won the case, the judge Mr Justice Cresswell said the market was run with "staggering incompetence".
Lloyd's itself is not directly involved in the commission's inquiry.
EC internal market spokesman Jonathan Todd said the complainants essentially alleged the UK authorities had failed to properly apply certain supervisory and auditing processes required by the EC's first non-life insurance directive.
Todd added: "What we are examining is the UK government's application of these rules which covered Lloyd's during the 1980s. We are seeking assurances that the directive was applied correctly."
Failure to properly apply a Brussels' directive could land the UK government in the European Court of Justice.
However, Todd stressed that Brussels had not yet started legal action in this case but was pursuing formal inquiries.
