Reinsurance rates will rise by 30% to 40% after last week's terrorist atrocity in the US, with conservative estimates suggesting the final cost of the overall tragedy will be between £20bn to £50bn.
Lloyd's spokesman Adrian Beeby said: "Rates have gone up already, with aviation hull seeing ten-fold increases."
A senior market source said reinsurance rates were going to rise 15% to 20% this year anyway, but would now double.
As Insurance Times went to press, airline officials on both sides of the Atlantic were in crisis talks with their respective governments.
US president George W Bush was reported to be looking at an "array of options" for US airlines, while British Airways and Virgin were lobbying UK Transport Secretary Stephen Byers for state aid if their US and European counterparts are bailed out.
Amlin announced on Tuesday it expected insurance cover for airlines to go up 400% and carriers will be unable to get third-party cover for their planes.
Moody's Investors Services has reported an "acceleration of price increases already under way within the commercial insurance and reinsurance markets".
The agency also said the industry's reported $10bn (£7.5bn) aggregate of losses would "prove to be insufficient, perhaps by a substantial amount".
Last week, wild figures ranging from $10bn (£7.5bn) to $100bn (£75bn) spread across the global insurance sector.
One analyst with a major UK bank said the economic downturn could bring "the worst recession in living memory".
But Fitch Ratings said the vast majority of insurers and reinsurers would be able to "absorb any losses without material damage to their financial positions". It said the high levels of financial strength and credit quality throughout the insurance and reinsurance industries should help see companies through these difficult economic conditions.
At this early stage it is becoming clear the London Market will feel significant pain. Swiss Re has reported a £680m blow and Munich Re is exposed to £600m losses. Lloyd's has admitted that capacity will be a problem.
Beeby said: "Managing agencies are putting up capital for next year. But if they suddenly have to pay bigger losses, they may not have the capital to increase capacity. There will be the question about whether or not they will meet pre-emptions to raise capital to meet those requirements.
"Capacity depends on whether or not a managing agency has significant capital. It will be a syndicate-by-syndicate decision. But it is too early to understand the full impact," he said.
"The impact will fall on the 2000 to 2001 year account. Capacity shortage is a possibility, but the business being written will be extremely profitable."
It was confirmed on Tuesday (September 18) that Lloyd's second capacity auction of the year has been postponed.
One Lloyd's insurer, Hiscox, cannot give any firm figures on its exposure because the company is expecting its broker, Willis Global, to give it an estimate of its loss.
Director Robert Childs said: "We are waiting to hear whether they will classify the attacks as being two events or just one. If there are two losses, we will have different exposure."
According to figures from Merrill Lynch, the company's exposure is £20m.
