The hull of the yacht Cheeki Rafiki, which went missing a week ago with four British sailors on board, has been found by the US navy, the UK Foreign Office has confirmed. Officials said there was still no sign of the missing yachtsmen and the search had been suspended after the life raft was found unused and still attached to the vessel.

Steve Warren, 52, from Bridgwater, Somerset, Andrew Bridge, 22, from Farnham in Surrey, James Male, 23, from Southampton, and Paul Goslin, 56, from West Camel, Somerset were sailing in a treacherous stretch of ocean from a regatta in Antigua to Southampton on 16 May when their yacht capsized and they went missing.

Bridge's family said in a statement that they are "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 coastguard, the Canadian coastguard, 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."

David 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 coastguard 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."

Early on Saturday morning the Foreign Office confirmed the search for survivors had been called off. "I am sad to confirm that the search for the Cheeki Rafiki has now been suspended," said Hugh Robertson, the Foreign Office minister for North America.

"My sincere condolences go out to the families of James Male, Andrew Bridge, Steve Warren and Paul Goslin at this very difficult and distressing time."

In a statement on Friday evening the USCG said there was nothing in the wreckage's discovery to suggest the crew would still be alive. "Navy crews observed that the sailing vessel's keel was broken off, causing a breach in the hull.

"The US coast guard has confirmed the life raft aboard the capsized sailing vessel Cheeki Rafiki was secured in its storage space in the aft portion of the boat, Friday, indicating it was not used for emergency purposes.

Damage to the hull of the Cheeki Rafiki.

"A US navy warship smallboat crew and surface swimmer captured underwater imagery clearly identifying the raft in its storage space. The image was shared with and acknowledged by the families.

"The US coast guard made an announcement, Thursday, that search operations would be suspended at midnight Friday unless new information or sightings suggested the crew would still be alive. None of the current developments indicate that to be the case."

It said a US navy warship helicopter crew discovered the overturned hull 1,000 miles off Massachusetts. A close inspection of the debris confirmed the identity of the yacht, which had been flooded.

It said: "The swimmer determined the boat's cabin was flooded and windows were shattered, contributing to the complete flooding inside.

"The swimmer also knocked on the hull and reached an arm's length below the waterline with no results. Surface swimmers are not trained divers and do not perform sub-surface operations."

Early on Saturday morning the Foreign Office released a statement on behalf of Stephen Warren's family. "We are very sad that the US has now suspended the search for Stephen and his friends," they said.

"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."

On Friday the sister of one of the four missing yachtsmen had expressed disappointment at the US coast guard's decision to call off the search if nothing was found by Saturday morning.

Relatives of the four missing yachtsmen in London. Photograph: Nick Ansell/PA

Kay Coombes, who fought against the initial decision last Sunday to suspend the search, which was reversed in the face of public pressure and intervention by the UK government, said her only hope was that they would find her brother Steve Warren and the others before the deadline.

Captain Anthony Popiel, chief of response at the 1st cast guard district, said on Thursday that he had informed the families the operation would be suspended at midnight on Friday (5am Saturday BST) if there were "no further developments to indicate search efforts would locate the crew alive".

Submerged hull of the Cheeki Rafiki.

The search was initially halted on Sunday morning when US officials said the crew would not have survived longer than 20 hours, only for it to resume on Tuesday after the men's friends and relatives accused the US of giving up too easily and started a petition that reached more than 230,000 signatures.

Searchers from the US coast guard, the US air force, the Canadian military and the British RAF, as well as a number of commercial vessels and volunteers, have combed more than 17,000 square miles of ocean in the hunt for the Cheeki Rafiki's crew.