The investors - known as names - had challenged an attempt by Lloyd's to recover money for its rescue vehicle, Equitas, in the High Court. Equitas was formed in 1996 to reinsure more than pounds 10bn of losses made between 1988 and 1992.
The Names claimed Lloyd's had used inaccurate records in an effort to assess their debts, including amounts not owed to Equitas.
Lloyd's admitted it had made mistakes in assessing the amounts owed to Equitas, including other debts which were owed to Lloyd's itself. But the judge, Mr Justice Tuckey, said the records were now in order.
The judgement opens the way for Lloyd's to extract payment from those Names who have not contributed to the 1996 agreement, which settled Lloyd's massive debts.
Ron Sandler, Lloyd's new chief executive, said: "This is an important decision in assisting Lloyd's debt recovery from Names who did not accept the reconstruction and renewal programme. It will be welcomed by all those members - over 94 per cent - who accepted the settlement offer and met their liabilities."
When the settlement was first announced in 1996, nearly 2,000 names resisted, effectively leaving other Lloyd's names to pay the bill on their behalf. However, Lloyd's yesterday said it had reduced this number to 800, including the 600 who went to court.
A spokesman for Lloyd's said the minority who had resisted the settlement were now looking at larger debts. This was because they had forfeited the right to debt credits offered to names who agreed to take part.