In 1971, the Robertson family set sail round the world on their boat Lucette. In the middle of the Pacific ocean, a school of killer whales capsized them. They survived for 37 days in a 9ft dinghy, till a Japanese fishing boat rescued them

Thirty-seven years ago this summer, some fishermen spotted a small dinghy adrift in the Pacific ocean. She was called the Ednamair and measured just 9ft from bow to stern. The fishermen watched the dinghy pitching and rolling in the vast emptiness of the Pacific and assumed that the occupants were long gone. They were nearly 300 miles from land. But they were wrong. A family of five, plus a friend, were on board. Packed like sardines into every nook, and with the flimsiest of protection, they had spent nearly six weeks stranded in the middle of the ocean with little food and water. Their dream of sailing round the world had gone horribly wrong.

On 27 January, 1971, Dougal Robertson, his wife, Lyn, and their children, Douglas (then 17), Anne, (16) and twins Sandy and Neil (nine), climbed into their yacht Lucette at Falmouth harbour, Cornwall. Eighteen months later – and by now joined by Robin, a hitchhiker, but minus Anne, who had left the boat in the Bahamas – they were 200 miles from the Galápagos islands when catastrophe struck. The Lucette was attacked by killer whales. "There was a bang! Bang! Bang! And we were lifted off our feet," recalls Douglas. "There was a huge splashing noise behind me and I turned round and saw three whales." It took only minutes for the Lucette to sink.

Bemused, shocked and unprepared – Lyn was still in her nightdress – they scrambled aboard a leaky raft, and then, when that deflated 17 days later, the dinghy. The odds of survival were against them: there was only enough water for 10 days, the only food on board consisted of a bag of onions, a tin of biscuits, 10 oranges, six lemons, and half a pound of glucose sweets. Nobody knew they were missing. They weren't on a shipping route, so their chances of being sighted and rescued were remote. Sinking was a constant worry due to the weight on board and to compound their problems, sharks were circling in the water.

Yet, amazingly, they did survive, and their remarkable story is legendary, inspiring a bestselling book – Survive the Savage Sea by Dougal Robertson – an exhibition and a feature film starring Robert Urich and Ali MacGraw (1992).

But according to Douglas, the real story of the Lucette is still a secret. He says his father's book only covers the days after the shipwreck, and is dry and academic, drawn from the voyage log. The film was only loosely based on what happened – "They sailed from Australia, not England!" – and while he wrote a book himself, The Last Voyage of the Lucette, in 2005, revealing the whole story, not many people heard about it because its publication was eclipsed by a personal tragedy. Douglas's son, Joshua, 16, had a near fatal motorbike accident in Australia. When Douglas should have been promoting his book, he was by his son's side in intensive care.

I meet Douglas, now 55, at a college in south London, where he works as an accountant. Except he doesn't look like an accountant; he looks like a biker, with black leathers and cowboy boots and a red biker scarf tied around his neck. He says this contradiction is a legacy from the wreck. "One part of you craves normality but the boundaries have been moved so far you can't really do that." He is stocky and strong-looking – even as a youth he was the "muscles on the boat", rowing, splintering wood, and blowing up the leaky raft until his mouth was cut and sore. "My dad was the brains. He couldn't have done that stuff without me." This is one of the beefs he has with his father's book. "We all contributed to the survival in the raft and nobody else was recognised for it."

His own book charts the family's transition from farmers to sailors and the 18 months at sea before the wreck – they were, it transpires, almost killed within hours of leaving Falmouth when they sailed into a Bay of Biscay storm. The book adds an intriguing emotional dimension to the story – eagerness and joy, but also a son's frustration and fear.

"Dad was a bit of a tyrant and we lived under his command," Douglas explains. "He gave us a good thrashing every time we stepped out of line, and he had hands like spades." The Last Voyage of the Lucette is a catalogue of his violent explosions. Douglas is punched in the face when the crockery smashes after not being stowed away properly, and he is pummelled into submission. But Douglas gets his own back. En route to Jamaica, his father is almost washed overboard after being hit on the head by the boom. Douglas rescues him by grabbing his legs, but as his father hangs perilously over the side of the boat, Douglas extracts a vow: "Promise you'll never hit me again, ever, or so help me I'll dump you over the side right now."

Then there is Albert, a male nurse they met in Miami. "Albert was a very nice man, a very friendly man," Douglas recalls, "but he had a motive – me." He says he still feels let down that his father didn't protect him. The book alludes to "inappropriate sexual connotations" but is hazy about specifics. Did Albert make a pass at him. "Yeah, he did." Did he succeed? "Somewhat, yeah," he says, quietly.

He says he tried to tell his father, but "he didn't want to listen. Neither did my mother. I started to tell my mother about it many years later and she said, 'Douglas, don't give me a burden to take to my grave.' So how can you tell parents like that what is happening?"

Yet he reveres his father, too, and aspires to be adventurous like him – although his brother, Neil, confirms that Douglas is a much gentler character. "I haven't undermined my dad – I've championed him for what he did for us. Dad was a very courageous man. He would never have got us home otherwise. But I've shown that he is a human being and he made mistakes." Dougal Robertson died in 1991 but Douglas insists that he had his blessing to write the book.

The youngest of eight children, Dougal Robertson had been a master mariner in east Asia, but gave it up after meeting his wife, Lyn, in Hong Kong in 1952 to become a farmer. To understand how the Robertsons survived their ordeal, you only need look at their previous life at Meadows Farm, in Staffordshire. It was a lesson in deprivation. No running water or electricity until Douglas was 10. No TV, set, only paraffin lamps and candles. No money for children's shoes. "Dad's life was terrifically hard," says Douglas. "He was very frustrated – he saw his brothers and sisters sending their children off to university and private school, the sorts of things he was no longer able to provide." Douglas is still critical of this decision. "He was a professional man and he became a farmer. I wish he'd stayed a professional man."

Douglas believes, most fervently, that this frustration was behind his father's violent outbursts. It certainly made him disposed to want to begin again. So when Neil, then nine, asked why they couldn't sail around the world like the yachtsman Robin Knox-Johnston, Dougal leapt at the idea. As did Douglas. "I wanted to go to university and be a geologist, but sailing around the world seemed a much better option," he recalls. The only person with reservations was his mother. "She was aware of the dangers. She considered the risk. For Dad it was an escape, so he didn't consider the risk. They argued about it. Mum probably hoped it would be a passing phase, but then we sold the farm."

One of the great surprises is that they set off from Falmouth astonishingly unprepared. Dougal was an experienced sailor and Anne had learned the basics, but the children had no experience whatsoever. "I still can't believe that!" cries Douglas. "Why didn't we learn to sail in those quiet waters at Falmouth? We went straight into a force 10 gale and it was horrific. I had no idea what to do."

But then no amount of experience would have prevented the whale attack. "I'm sure they thought we were a big whale. Maybe it was the shape of the hull or the speed we were moving at," he says. His most terrifying moment was yet to come – swimming in the water to the raft, after the Lucette went down. "I'd seen the whales in the water. I thought, 'This is how I'm going to die. I'm going to be eaten alive.'"

Once on the raft, he and his father came up with the plan that saved their lives: rather than aiming for land, they decided to aim for water – which meant sailing 400 miles north to the Doldrums.

Life on the raft was grim. "It got holed when we launched it and that hole got worse. We were sitting with the water up to our chest. We had salt-water sores all over us and the heat would be taken out of your body – it was horrible. We used to take it in turns to sit on the thwart [seat] because it was dry, and my mum, God bless her, would say, 'Doug, you take my turn.' And she'd sit in the water for another hour." Sleep was impossible, because as soon as they nodded off, their heads would hit the water and they'd jump awake. Lyn was terrified that the twins would drown in their sleep.

The Ednamair, by contrast, was dry but flimsy. "We were always in danger of being swamped by a wave, and on the 23rd day it rained so heavily we thought we'd lost it. I think Dad was ready to give up. But Mum looked at Dad and held his eyes. Then Dad said, 'Bale for your lives and bale twice as quick as you're doing now.' And we did."

What kept them going was grit, determination and turtle blood. "You have to knock it back quickly, otherwise it sets into blancmange," Douglas explains. Plus it's got an "aftertaste that makes you want to wretch". Their mother rubbed turtle oil on the salt-water boils, and tried to keep them all hydrated with makeshift enema tubes made from the rungs of a ladder. "It was her nursing background. She knew the water at the bottom of the dinghy was poisonous if taken orally because it was a mixture of rain water, blood and turtle offal. But if you take it rectally, the poison doesn't go through the digestive system."

By the time the Toku Maru, a Japanese fishing boat, rescued them after spotting a distress flare, they were so dehydrated that they hadn't peed for 20 days and had tongues so swollen with thirst that they could hardly speak. "It was like having our lives given back to us, a pinnacle of contentment never reached again," says Douglas. When they got to Panama, he celebrated with three rancher's breakfasts of steak, eggs and chips.

After they got back - another voyage on board the MV Port Auckland – the family lived in a caravan on an aunt's farm in the Midlands for six weeks. When Dougal got an advance from his publisher, they moved to a rented cottage. But Douglas says that family life was changed for ever. "Mum and Dad divorced. They couldn't be together after that." He says they had terrible arguments on the dinghy.

"My mother's fault I'm afraid," says Douglas. "She'd argue about not having electricity at the farm and not having proper running water or shoes for the kids, and Dad didn't need that."

Dougal bought another yacht and went to live in the Mediterranean. Lyn went back to farming, on a farm bought for £20,000 by Dougal from sales of Survive the Savage Sea.

Douglas believes his parents never stopped loving each other. Dougal died from cancer, aged 67, and for the last three years of his life, Lyn nursed him at their daughter's house. She died aged 75, also from cancer. Douglas went on to join the navy, and then became an accountant. He has five children from two relationships.

"Dad always felt guilty," concludes Douglas. "He always said, 'I don't know why I did it. I could have taken you to the Mediterranean – that would have done. I didn't have to take you around the world.' But we would say, 'Dad, we survived! You helped us! We did it!'"

The Last Voyage of the Lucette by Douglas Robertson, Seafarer Books, £13.95. To order a copy for £12.95 with free UK p&p, go to theguardian.com/bookshop or call 0330 333 6846. The Ednamair is on display in the Survival Zone at The National Maritime Museum, Falmouth, until January