Lloyd's capacity for the 2002 year of account will be £12.3bn. The amount of premiums the 300-year-old market can write will rise from £11bn.
Lloyd's chairman Sax Riley said: "We now have our largest ever capacity. Our capital providers are voting with their chequebooks.
"Having come through a number of difficult years, they are now increasing their underwriting commitments as we enter a period of sustained market growth."
Prior to 11 September, syndicates were requesting pre-emptions, which would have taken the market upto £13bn to £14bn. Many insurers have now invested their capital in tax-free Bermuda.