The Paying Names Action Group (PNAG) said that the American Names' Association (ANA) has advised its members to support PNAG in applying for a judicial review of Lloyd's reconstruction and renewal plan.
PNAG has said it has about 3,000 members, but industry sources reckon this may be an overestimation since official documents issued ahead of the review indicated it had under 1,300 members.
The ANA claims to represent around 500 of the 3,000 names. This group has opposed the recovery plan for some time.
"I am very pleased to have support in our efforts to redress the balance of fairness in Lloyd's current R&R offer," said the PNAG chairman, Tony Welford, who has led this latest legal challenge.
The case is due to be heard in the High Court on Monday and comes as the 33,500 names at Lloyd's decide whether to support the plan and pay final bills to reinsure billions of pounds of liabilities into a new company, Equitas.
PNAG believes the recovery plan is unfair to names who have continued to meet cash calls from Lloyd's and trade on in the market after 1992 - the cut-off for reinsurance into Equitas.
David Rowland, the Lloyd's chairman, has written to names, in a letter dated 8 August, reiterating his "regret'' that PNAG has proceeded to apply for a judicial review.
He repeated that Lloyd's could not improve further on a pounds 3.2bn settlement offer to names. Lloyd's plans to send further details to names on Monday.
They will receive a breakdown of how personal stop loss policies have affected their final bills and learn the size of their funds at Lloyd's as of 12 July - assets they have pledged in backing business underwritten at the market.
The Association of Lloyd's Members plans to release on Monday a report from solicitors Wilde Sapte, expected to back key elements of the recovery plan including Equitas.
Rebel names are furious that, having shouldered years of losses due to asbestos claims and the like, they will be left out in the cold by the settlement.
Names have until 28 August to accept or reject the settlement offer and until 30 September to pay final bills.