Lloyd's has estimated that its total losses from the September 11 terrorist attacks on the US will be £1.3bn.
But it said it still expected to return to profitability by 2002 or 2003, thanks to sharp rises in insurance rates.
Lloyd's chairman Sax Riley forecast the losses to the insurance industry would reduce the number of firms willing to offer cover in high-risk environments, which would cause a rise in premiums.
He said Lloyd's was strong enough to cope with the US claims due to a major restructuring in recent years and moves to increase the market's capital.
"While a figure of this size will have a significant impact on the Lloyd's market, the market's strong capital base will absorb this loss," he said in a statement.
So far, only US insurer Berkshire Hathaway has estimated larger losses as a result of the attacks – $2.2bn (£1.5bn) before tax.
Lloyd's said its exposure was equivalent to 12% of the market's 2001 capacity. It is underpinned by $27bn (£18.4bn) of assets, including money held in its central reserve fund and money invested by its members.
