He also said Lloyd's was at the "limit of our resources", and that there was no prospect of the rescue being topped up by the pounds 100m that Tony Welford, chairman of the group, suggested was needed.
He questioned whether the action group had the mandate it claimed from its 3,000 members, who would be unable to accept the rescue offer if they continued with the litigation.
The toughly worded response came hours after the action group lodged papers at the High Court, taking the first steps towards a judicial review.
There is expected to be a hearing early next week at which a judge will be asked for leave to proceed to a full hearing.
The group's case is based on the fact that some members who paid their debts benefit less from the rescue plan than those who refused to pay.
John Abramson, of Warner Cranston, solicitors, said one of the remedies the names were seeking was an injunction. Lloyd's sources suggested that if an injunction were requested, the market would demand the rebels lodge a bond covering the potential costs of blocking the rescue, which could run into billions.
Mr Welford said: "We don't want to bring the house tumbling down - after all, we are the most loyal supporters of Lloyd's, since we paid out bills.
"Our only objective is to make Lloyd's realise they have to talk to us."
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