The 200 Jaffray Names confirmed this week they are planning to sue Lloyd's for about £100m.
This follows the Court of Appeal decision last month that found Lloyd's not guilty of fraud, upholding an earlier High Court decision in November 2000.
But, while the court ruled there was insufficient evidence to find Lloyd's guilty of fraud, it was found to have made misrepresentations in its brochures.
United Names Organisation (UNO) Co-chairman David Harris said: "This opens the door for us to sue under negligent misrepresentation.
"The next step is there will be a directions hearing before the Court of Appeal at the end of October," he said.
However, Lloyd's is confident it can protect itself in the event of future litigation.
A spokesman said the market is protected by the 1982 Lloyd's Act that grants it immunity from a range of actions. He cited the Limitation Act that prevents lawsuits being brought for negligence after six years.
"Ultimately we believe they have no legal grounds to stand on," he said.
UNO disagrees. "We are not suing them under the Lloyd's Act, but under the Misrepresentation Act," Harris said.
"As for the [limitations] statute, our case has been running from before six years had elapsed.
This is an amendment to the original pleadings, which we could not make formerly because Cresswell had ruled that no misrepresentations had been made," he added.
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