The level of acceptances was revealed as Lloyd's prepared to appeal tomorrow against an injunction granted in a state of Virginia court last Friday that had threatened to derail the pounds 3.2bn rescue package.
The injunction, which demanded that Lloyd's produce more information for 93 of its American names, effectively ruled out the possibility of securing the agreement of all American members by the deadline for acceptances, set for noon on Wednesday.
Mr Rowland said yesterday: "I am confident that by the deadline the offer will have been accepted by the overwhelming majority of our members. The position we are in at the moment is that we already have, from the votes that have been cast, the knowledge that the majority of the members wish to go ahead."
Lloyd's members who have not yet accepted the deal have been warned that failing to do so will leave them outside any settlement. The deal offers Lloyd's members debt write-offs of pounds 2.1bn and a litigation settlement fund of a further pounds 1.1bn. Many US members have already accepted the offer.
An appeal against the Virginia injunction is due to be heard in the Federal Appeals Court in Baltimore, Maryland tomorrow. Failure to overturn the decision could leave Lloyd's with a funding deficit of up to pounds 200m. If that were the case it would risk failing a solvency test set by the Department of Trade and Industry and due to take place at the end of this week.
Mr Rowland remained confident of victory on appeal: "We have to remember that we've had countless actions in the United States. We won all the key ones to do with Lloyd's and I'm absolutely certain that the Court of Appeal will actually see the good sense of what we're doing and support us."
Lloyd's is understood to have several contingency plans in place to ensure the rescue package goes through. One option is to exclude the American names and replace their funding with bank borrowings.
At the heart of the Virginia ruling was a claim that American names needed more information before they could decide whether to approve the restructuring package.