The threat to the rescue comes as letters go out from David Rowland, the Lloyd's chairman, to 34,000 names, spelling out the final cost to each of them of the proposals.
The Paying Names Action Group, representing 3,000 names who have paid all their losses, has instructed solicitors to apply to a High Court judge in "the next few days".
The group is angry that many names who have paid their debts in full are being treated more harshly in the rescue than those who refused to pay.
The best-known case of differing treatment between paying and non-paying names is that of Peter and Colin Vine, 80-year-old twin brothers who have exactly the same participation in Lloyd's syndicates.
The brother who paid his debt to the market is said to face a bill pounds 125,000 higher than the one who refused.
The action group will be asking a judge to rule on whether the Lloyd's plan is eligible for a judicial review. If this is agreed they will press for a full hearing before 28 August, the final date for members of Lloyd's to vote on the plan.
John Abramson of the action group's solicitors Warner Cranston said: "I am instructed to proceed." Tony Welford, leader of the action group, said: "We are preparing our affidavit."
A judicial review is normally possible only when an authority makes decisions on the basis of statutory powers. The action group has been advised that the Lloyd's Act establishes the market's ruling council as a statutory body, and that as a result its decisions can be questioned by judges.
The action group wrote nearly a fortnight ago to Ron Sandler, chief executive of Lloyd's, setting out their objections to the rescue plan, arguing that Lloyd's had misconstrued its powers and demanding greater parity between names who have paid and those who have not.
Mr Welford said at the time that his members had deep pockets to pay for legal action. The letter asked for a reply within seven days.
The six-page reply from Lloyd's, received yesterday, challenged the action group to go to court by rejecting the claims "vehemently and vigorously", saying they would be strongly resisted.
Mr Rowland has publicly acknowledged that there is some "rough justice" in the settlement but Lloyd's says it has gone as far as it can in reducing anomalies.
Earlier this month Lloyd's won an overwhelming vote in favour of the first steps towards the rescue when members approved a pounds 440m contribution towards it.
But to get it through, Mr Rowland must also persuade syndicate action groups - though not the Paying Names Group - to give up their lawsuits against the market, in a series of votes in the coming weeks. The vote by all 34,000 members is the final stage.
As well as the threat of judicial review, there are also complaints from members that despite the letters this week detailing their circumstances many will not know the full cost of the rescue plan until after the 28 August deadline for the vote.Reuse content