Cautious underwriters at Lloyd's are only offering 15 days' cover for various classes of business, particularly fine art and property.
This follows the September 11 attacks and the war in Afghanistan.
Hiscox underwriter Annabel Fell-Clark said the limited cover was immediately imposed on the fine art market after the World Trade Centre (WTC) attack, but had now spread across the shaken London Market.
"It started in the art market, but it is really across the board now. From an underwriter's point of view, it is difficult to commit to specific policy issues when people are blowing each other up all over the world. That is why we are seeing only 15 days' cover and then the policy is reviewed.
"During the two days following the attack, many Lloyd's underwriters regarded the UK and the US as uninsured.
"To put it in perspective, a couple of days before the attack, there was $11.5bn (£7.95bn) capacity for the art market in the London Market. Today, there is just $400m (£276.5m) capacity in Lloyd's for fine art risks," she said.
Many famous paintings involved in major exhibitions are now stuck in galleries around the world. Three works by Dutch master Vermeer, which were on show at the UK's National Gallery, cannot be moved.
A spokeswoman for the National Gallery said: "The Vermeers and a number of other works have remained at the gallery because of their fragility. The gallery and owner thought it was too unsafe to travel."
Two exhibitions at the New York Armoury have been cancelled so far. "These had to be cancelled because the space was being used as a recovery and body-bag centre," said Fell-Clark.
Estimates of the cost of losses incurred to fine art and antiques that were destroyed when the WTC collapsed is $100m (£69.1m). Sculptures by Auguste Rodin and paintings by Joan Miró and Roy Lichtenstein have been reported lost.
AXA Art, the specialist fine art division of the French insurer, has put aside £20m to cover losses of three collections held at the WTC, including the Cantor Collection, housed at the Cantor Fitzgerald offices.
AXA Art development manager Clare Pardy said: "We are trying to give a positive message of continuity to our clients. We don't wish to panic people, so our policies remain unchanged and we will assess each risk individually."