Relatives of one of the missing British crew of the Cheeki Rafiki have said they are “shocked and deeply saddened”, and their condolences go out to the other families.
Hopes of finding the four men have all but faded after the yacht’s life raft was found on board the capsized vessel.
The US Coast Guard called off its search at midnight (3am British time), and an RAF Hercules plane due to hunt for the four sailors will not now go out.
Underwater imagery taken by a swimmer from a US Navy warship showed the raft clearly stowed in place, indicating it had not been deployed in an emergency.
Prime Minister David Cameron said his “thoughts are with the families and friends of the crew”.
The upturned yacht was discovered in the Atlantic Ocean yesterday, about 1,000 miles (1,609km) east of Cape Cod in Massachusetts.
Its cabin was completely flooded and its windows were shattered. There was no sign of survivors.
Coast guard officials decided to call off the search for the men - experienced captain Andrew Bridge, 22, from Farnham, Surrey, and crew members James Male, 23, from Southampton, Steve Warren, 52, from Bridgwater, Somerset, and Paul Goslin, 56, from West Camel, Somerset - unless there was new information or sightings which suggested they would still be alive.
But “none of the developments indicate that to be the case”, a spokesman said.
Mr Bridge’s family said in a statement: “We are obviously shocked and deeply saddened by the news.
“Andrew will be dearly missed by everyone who knew him. Our thoughts and condolences go out to the families of the rest of the crew on the Cheeki Rafiki.
“We would like to thank everyone who’s helped in the search for Andrew, including the US Coast Guard, the Canadian Coast Guard, the RAF, merchant vessels, the yachting community and the British and American Governments.
“We have been overwhelmed and strengthened by the public support we have received and would like to thank the media for their support and treating us in a respectful and dignified way.
“We will not be making any further comment at the moment. We would ask just for privacy at this difficult time.”
Mr Cameron said: “My thoughts are with the families and friends of the crew of the Cheeki Rafiki after the sad news that its hull has been found with the life raft unused.
“My sincere thanks to the US Coast Guard for leading the international search with great dedication - and to the US Navy, the Canadian authorities and to our own RAF C130 aircraft who took part in it.”
A coast guard spokesman said: “After a navy warship relocated the overturned sailing vessel on Friday, search planners confirmed the boat’s life raft was secured in its storage space in the aft portion of the boat, indicating the crew had not been able to use it for emergency purposes.”
He added: “The crew and swimmer deployed to investigate the overturned boat after a helicopter crew located it 1,000 miles off Massachusetts and within the US Coast Guard’s search area.
“The navy surface swimmer determined the boat’s cabin was flooded and windows were shattered, contributing to the complete flooding inside.”
The surface rescue swimmer also knocked on the hull and reached below the waterline, but with no results. Navy crews saw that the Cheeki Rafiki’s keel was broken off, causing a breach in the hull.
Official British efforts to find the missing men have also now been cancelled.
A spokesman for the Foreign Office said: “The UK C130 was due to search for one more day for the life raft of the Cheeki Rafiki.
“In light of the US Coast Guard’s decision to suspend their search for the crew following photographic confirmation that the life raft is in the hull of the boat, the C130 will now return to the UK.”
A statement on behalf of Mr Warren’s family said: “We are very sad that the US has now suspended the search for Stephen and his friends.
“From the beginning we, together with the other families involved, have continued to hold out hope that he would be found alive. The US Coast Guard have led an exceptional search.
“This is now an incredibly difficult time for all the family. We would therefore request that we are given privacy to come to terms with today’s decision.”
The families of all four sailors asked for their privacy to be respected.
The men were on board the 40ft (12m) yacht when it is thought to have got into trouble around 620 miles (998km) east of Cape Cod on May 15 as it was sailing back to the UK from a regatta in Antigua.
The US Coast Guard resumed its search for the missing men on Tuesday morning having previously suspended it after scouring 4,000 square miles (10,360 sq km) of the Atlantic, following a petition in the UK which attracted 200,000 signatures and pressure from the UK Government.
The hunt for the missing men was finally called off after military search teams from the US, Canada and the UK, as well as numerous commercial vessels and volunteer yacht crews combed an additional 21,000 square miles (54,390 sq km) of sea.
A coast guard spokesman said: “Based on the extreme sea conditions at the time of distress, but assuming best-case emergency equipment, the estimated survival time past the time of distress was approximately 20 hours.
“Searches were suspended nearly 200 hours after the time of distress.”
Captain Anthony Popiel, 1st US Coast Guard District chief of response, said: “It is with sincere compassion for the families of these four men that our thoughts and prayers are with them all during this difficult time.
“The US Coast Guard is always hopeful, and makes the utmost efforts to find and rescue those in peril. We have the greatest appreciation for the US Navy and US Air Force for working with us alongside the militaries of Canada and the United Kingdom during this massive search effort.
“It is only after our deepest consideration that we suspend our active search efforts.”
Jeremy Wyatt, spokesman for the World Cruising Club based on the Isle of Wight, told BBC Breakfast: “I think we have to be realistic and face facts that they’re not in a raft and therefore the chances of finding anyone are non-existent now.
“In some ways it’s a hard fact, but I think, after a week of searching, it’s really the only conclusion you can safely draw.
“At least by finding the hull that has given answers to the question so in some ways it’s providing some form of closure for the families. They can build up a narrative in their own mind of what’s happened.”