A British couple held hostage by Somali pirates are warning that their lives are in danger after their captives threatened to kill them if their ransom demands are not met within a week.

A new video aired on Friday by the British's Channel 4 showed the pair couple, Paul Chandler and his wife Rachel, standing in front of numerous gunmen brandishing their guns while they make direct appeal to the camera.

Paul said his captors are treating them well but warned that the hospitality may come to an end within a week if the ransom demand is not met.

"We are also concerned that these people will lose patience and will not feed us, and I have no doubt that they will not hesitate to kill us, perhaps within a week or so of now if there is no response," he said. "So, please somebody get in touch. Otherwise we just sleepwalk to a tragic ending."

The couple were kidnapped from their 38-foot yatch, Lynn Rival by armed pirates on October 23 while on vacation in the Indian Ocean. They were taken to Harardhere, a pirate haven in northeastern Somalia. Their empty yacht was later found abandoned in the international waters.

The Somali pirates have demanded $7 million in ransom, which the British government has since declined to pay.

"The government will not make substantive concessions for hostage takers, including the payments of ransom," said an official statement from British Foreign and Commonwealth Office.