The woman, believed to be in her thirties, was swept 50 miles off the coast of Honduras. The rescue operation began after the United States Coast Guard in Miami alerted HMS Sheffield to the position of what was assumed to be a body in the waves. She was plucked to safety by a helicopter from the frigate at 8.30pm on Tuesday.
Speaking from the Sheffield yesterday, Lieutenant-Commander Mark Folwell said: "It's quite incredible. To have not only the physical strength to do that, but also the mental capacity to survive is absolutely remarkable."
The woman was on a drip, receiving antibiotics and being treated for hypothermia. She was "drifting in and out of consciousness" but crew members had managed to find out a little of what happened to her.
"Basically, she was on the mainland, which is 50 miles from where she was found, and when Hurricane Mitch went over the southern Caribbean she and her husband and three children were washed out to sea," said Lt-Cdr Folwell.
Hurricane Mitch has killed at least 9,000 people throughout Central America, about 7,000 of them in Honduras. Floods and mudslides have devastated communities across a 500-mile corridor from Nicaragua into southern Mexico, and from the Caribbean coast of Honduras to the Pacific. Many survivors have been left without homes, food or power. In response to appeals for one of the worst natural disasters to hit Central America, Britain has pledged pounds 500,000 of aid.
The Sheffield, which had been on drug-fighting operations in the Caribbean, has been helping disaster relief efforts since last Friday. It remained in the area yesterday searching for the other family members. Lt-Cdr Folwell said: "We have found no one else but we have seen lots of debris."
Initially, it was believed that the woman was a survivor from the Fantome, flagship of Windjammer Barefoot Cruises, which disappeared in the hurricane. The 282ft sailing vessel is skippered by Guyan March, 32, of St Austell, Cornwall. The Foreign Office confirmed that a Briton was among the 31 crew missing.
Debris, seven life-jackets and two empty life-rafts from the Fantome were found around the islands of Guanaja and Roatan, off Honduras. Coastguards have not given up hope of finding the crew alive.
Dr Michael Tipton, a reader in applied physiology at the University of Portsmouth and head of the environmental medicine unit at the Institute of Naval Medicine, said that the woman was "very, very lucky to be alive. This is the longest period anyone has survived in the water that I have heard of.".
The warm sea, the buoyancy provided by the wreckage the woman was clinging to and the insulating layer of fat covering her body will all have helped.
In a colder sea, no matter how hard she shivered or exercised, she would have rapidly become hypothermic as her body temperature dropped and she would have lost consciousness and drowned. But in a warmer sea of 25C or above it is possible to stabilise the body temperature by shivering.
Even in a warm sea, after several days without food or water, the body will run out of fuel to keep the muscles working. The length of time is determined by the effort needed to stay afloat and the layer of insulating fat keeping the body warm.
Dr Tipton said: "The fatter someone is the smaller the amount of heat they need to generate to maintain their temperature. Having something to keep her afloat would have helped, too. If she had been swimming she would have become exhausted much quicker."