A group of Names met legal representatives on Tuesday to discuss taking fresh action against Lloyd's.
The group, led by United Names Organisation co-chairman Catherine Mackenzie Smith, looks increasingly likely to take legal action.
This follows Lloyd's winning the Court of Appeal case against the Jaffray Names in July. The court found Lloyd's not guilty of fraud, but found that it had made certain misrepresentations to investors.
The Court of Appeal met again last week and awarded Lloyd's 85% of its legal costs relating to the Court of Appeal process, as well as an interim payment from the Names of £650,000.
Because the court originally found that Lloyd's had made misrepresentations, the Names hope to win compensation if a new case is brought on the grounds of negligent misrepresentation.
It is understood that sums awarded could be as much as £100m.