The co-chairman of the United Names' Organisation (UNO) and another member of its committee have applied to Lloyd's for details of its final settlement offer following the Jaffray case.
Catherine Mackenzie Smith is now awaiting a revised offer from the 300-year-old market, but her colleague's request has been turned down.
After Lloyd's victory in the Jaffray case, which dismissed Names' allegations that former senior members of the market had concealed escalating asbestos losses, the market said it would write off some of the £300m owed to it by more than 700 private investors.
According to Lloyd's, in addition to the two out of six UNO committee members, a further 133 global Names have applied or are now applying to participate in the settlement initiative since the offer was made in January.
But Chris Stockwell, adviser to the UNO, dismissed the claims.
"That is certainly not true," he said. "Out of our 200 members, only one has accepted and two others have been given an offer."
Another committee member, John Henderson, said: "Less than 25% of members have submitted an application and they need our consent in order to settle according to our rules."
Stockwell confirmed committee members had approached Lloyd's for a settlement offer and added that the UNO would be returning to court on October 8 to appeal before Mr Justice Clarke.
But he warned that if a deal was not reached by January next year, the organisation would launch a fresh legal battle.
Lloyd's spokeswoman Sara Chorley said: "We are delighted with the response so far."
