Lloyd's is losing out on market share because $25bn to $30bn (£17.5bn and £21bn) of capital is being invested in overseas insurance markets, according to analysts.
Fitch Ratings director of insurance Chris Waterman said since the World Trade Centre tragedy, new capital had flooded into insurance with the start up of new companies in Bermuda.
Other existing organisations had also raised more cash to take advantage of rate rises.
But Waterman said that Lloyd's, which has increased its capacity by £1.2bn since last year, is now losing business.
"We would expect capacity to be increased more than that, with rate rises being significant. The result is Lloyd's is losing market share."
He said between $25bn and $30bn had entered the insurance industry since
11 September and rates had gone up an average of 30% across the board. But the amount of business Lloyd's can write has only grown by 11%.
Benfield Group chairman John Coldman said: "Since the World Trade Centre, the introduction of new capital has been swift at about $28bn (£19.6bn)."
He estimated 50% of that funding had gone to 11 new Bermudan ventures.
