Relatives of four Britons who went missing when their yacht capsized in the mid-Atlantic Ocean have made an emotional plea to the US Coastguard to resume the search and rescue mission as they remain convinced that their loved ones are still alive.

The call by the yachtsmen's families for the search for the crew of the Cheeki Rafiki to be resumed has been backed by an MP as well as prominent figures in the sailing world.

The 40ft Beneteau performance racer/cruiser yacht, ran into difficulties some 620 miles east of Cape Cod in Massachusetts on Thursday while returning to the UK from a regatta in Antigua.

Contact with the ship's experienced captain Andrew Bridge, 22, and crew members James Male, 23, Steve Warren, 52, and Paul Goslin, 56, was lost in the early hours of Friday while they diverted to the Azores.

US and Canadian aircraft assisted by three merchant vessels looked for them throughout Friday and Saturday but called off the search yesterday at 5am local time amid treacherous weather.

Some 4,000 square miles were scanned for the "very well-equipped" vessel's two personal location GPS beacons until no more transmissions were received from the small devices, which have a short battery life.

On Saturday, a cargo vessel which was helping with the search spotted and photographed an overturned hull which matched the description of the Cheeki Rafiki but reported no signs of people on board or a life raft.

Kay Coombes, the sister of Mr Warren, a project manager for an electrical company, said that she and their mother, Margaret Warren, were convinced that he was still alive.

The 46-year-old said: "It's an utter nightmare, we are grateful for the US and Canadian coastguards for what they have done so far, but it's stopped too soon after two days, it's not long enough, we believe they are still alive.

"They are four strong-minded, physically strong sailors, they knew they were in difficulties and had every opportunity to get into the life raft which would have had provisions for several days. But if no-one is looking for them, they won't be found."

She added: "Everyone is just trying to put pressure on the US Coastguard using every channel possible. They said they would only continue the search when any debris was found but if no-one is looking how can they find it? There are only passing ships in a very big ocean."

She added that their mother was very upset and added: "It's very, very difficult, especially being so far away."

Mr Bridge's aunt, Georgina Bridge, said the family, including his parents David and Mary and brother William, 19, were shocked at the events.

She said: "Obviously we are all devastated by what is happening, we just want the search to resume.

"We have great appreciation for the efforts the US Coastguard and our Foreign Office have made but obviously we believe there is hope and there is a possibility of them being found alive."

Ms Bridge added her nephew was a professional sailor who was trained to survive such a situation.

Mr Bridge's mother, Mary Bridge, told the BBC: "I'm a bit numb actually. We wanted him back."

Her husband, David, added: "We all think they're in the life raft. One personal beacon was set off, and when that died they set another personal beacon off, which would suggest they were somewhere safe enough to be able to do so."

Caroline Nokes, the Conservative MP for Romsey and Southampton North, said that she had been told by the Foreign Office that it was "investigating every avenue it can do" to try to encourage the US Coastguard to act for longer.

Mr Male's father, Graham Male, said there was evidence that the crew had acted in a reasoned manner.

He told ITV Meridian: "The crew had plenty of time to prepare the life raft and from new evidence we have, there were two personal beacons on board, one of which was James', when they were set off they were set off in a timed position, they reserved their resources, they waited until the first beacon had run out before they actually set the second beacon - that's rational-thinking people."

Mr Bridge, who is from Farnham in Surrey, was being paid by Southampton-based yacht training and charter company Stormforce Coaching for his role as captain, a spokeswoman for the firm said.

He had taken part in Antigua Week together with Mr Goslin, from West Camel, Somerset, Mr Warren, from Bridgwater, also in Somerset, and Mr Male, from Southampton, all described as "very experienced offshore yachtsmen".

Sir Robin Knox-Johnston, the first man to sail single-handedly non-stop around the world, and president of the Sail Training Association, said that there was still hope for the sailors.

He said: "Everyone trains for this, every yachtsman goes and does a sea survival course.

"This was an experienced crew, they almost certainly would have done that, they would have known the score."

An online petition, set up by Nicola Evans, a friend of Mr Bridge, has gained more than 20,000 signatures calling on the US to resume the search.

The 38-year-old said: "He has a heart of gold, he's an amazing guy and deserves every chance to be found."

Amongst those who have signed the petition is Claire Goslin, the daughter of missing Paul Goslin. She wrote: "One of the sailors is my dad and we cannot give up! He is my world and we need to start this search again!!!"

Mr Goslin's wife, Cressida, t old BBC Radio 4's World At One programme: "The evidence suggests because they had time on board, they knew there was a water leak, they had time to prepare to put a life raft in the water... it was a life raft suitable for 12 people and there were only four people in there.

"They would have had the provisions that were in the life raft but they would have had time to take more provisions.

"We don't want to leave any stone unturned, it is a very short window of opportunity - we are realistic. If we had another two or three days and they don't find anything or they find bodies, or whatever happened, I think everyone would just feel they have some closure."

A Foreign Office spokeswoman said: "We are aware of a missing yacht off the east coast of the USA with four British nationals on board.

"We are in continual contact with the US Coastguard and are providing consular assistance to the families."