Like most six-year-olds and twins the world over, Savannah and Bella Mines are a joyful, fizzing handful.

Bella, 15 minutes the elder, is tomboy-boisterous and learning to play guitar. Savannah, more shy, is full of beans and into the piano. They are both mad about athletics, Peppa Pig, The Gruffalo…

And every single time their dad, Jamie, 39, reads them that favourite bedtime story, it is with a lump of gratitude in his throat.

A quadruple amputee after an horrific accident that almost killed him, the hands that now turn the pages, cuddle his girls and pick up after them aren’t the hands he was born with.

These hands didn’t hold his daughters in their first moments of life.

Instead they are an incredible, generous, life-changing gift that the single father from Bradford on Avon, Wiltshire, received when he had a double hand transplant.

They are transforming this young family’s life.

“Life is so good since my transplant,” he says. ““I used to have to flick the book pages with my stumps, not any more. It was amazing putting my arms around my daughters again, properly cuddling them for the first time since the accident.

"They ask me, when will you be able to draw with us Daddy? The answer’s one day soon, I hope. I am improving all the time.

“I’ve been on holiday, and gone swimming. And I look forward to all the things I’ll be able to do in the future.”

The day that changed everything for Jamie was December 19, 2016. It dawned wet and windy. Bella and Savannah were five months old, days from their first Christmas.

Jamie was off to his job at a scaffolding firm.

“I was a new dad and loving it. The nappies, the crying, I loved it all,” he laughs. “I’d even got used to the lack of sleep. It’s the meaning of life, really.”

A semi-professional footballer for 17 years, playing for the likes of Larkhall Athletic in Bath, he was fit and energetic, loving the hard, outdoor labour of his work.

After lunch, he was working on a five metre rig at a site in Swindon, lifting a sheet tin roof into place underneath power lines.

And suddenly, from the cables which were too close to him, 33000 volts of electricity arced and surged into his body.

“I remember it belting me inside and out,” he says. “My arms were swelling massively, my legs bursting against my combat trousers. The pain was unbelievable.”

Paramedics arrived, the wintry sky drummed with the beat of an approaching air ambulance.

Conditions were too foggy for the airlift, however. A cherry picker and stretcher ferried Jamie to an ambulance and from there to hospital.

“I thought, I’m going there and I’m going to die,” Jamie says.

But he also thought of his babies, waiting at home.

“There was an inner power inside me and it was for them. Their first Christmas was six days away. I had to live.”

The next days were a fog of sedation and fever dreams.

Jamie remembers trying to get out of bed, to find that his right leg had been amputated below the knee.

The toes and half of his left foot were also gone, that leg would eventually be amputated too. The accident took both Jamie’s hands and half his arms, too.

At first he despaired. “I wondered why they’d saved me,” he says. “I’d been a fit man, playing my football, doing heavy, physical work. Now I wouldn’t be able to hold my girls or brush their hair. All I could think of was the past.”

But it didn’t last for long. That inner strength and grit was still there, if his limbs were not.

His mum, Carla, 70, explains, “The surgeons thought he might last a week if he was lucky. But they didn’t know my Jamie. He was determined. He had those little girls at home and he loved those little girls so much.”

Through long months in ICU, where his children couldn’t come to see him, he focused on getting home to them.

“It was heartbreaking - would I ever be able to hold their hands or tickle them?” he says. “After seven months I was moved to the John Radcliffe Hospital in Oxford for rehab. At last, on the girls’ first birthday, they were able to visit me.

“They remembered me! They called me Daddy, and were laid on my chest. It was amazing.”

Finally, with two prosthetic legs, two prosthetic arms, Jamie was well enough to go home.

A single dad to Savannah and Bella since they turned two, it was a baptism of fire.

Severely disabled, still recovering, Jamie had two little lives depending on him.

“Changing one nappy took me 40 minutes and I had two to do each time!”, he says. “Pull-ups made that easier in the end.”

But his greatest fear did not come to pass.

“I was able to cuddle them with my stumps. I wore my prosthetic arms outside but Savannah and Bella didn’t like the claws so at home they came off.”

He was coping. More than coping.

His former firm, Boundary Scaffolding Ltd, had been fined £80,000 for the accident, its director receiving a six-month suspended sentence.

The compensation Jamie received allowed him to be the best dad he could.

To pay for help to wash his girls’ hair properly and do it nicely for school. To prepare meals…

But he never gave up hope of somehow holding, really holding, his children by the hand.

“I read everything I could about miracle transplants,” he says. “I did loads and loads of research and then the first double hand transplant operation took place at Leeds General Infirmary.”

Jamie sourced an email address for the pioneering Professor Simon Kay, who’d led the operation.

“With special technology that scanned my retina to enable me to type, I told him my story. He was in Sweden at a conference but he got back to me that same day.”

It was the start of another extraordinary journey, at the end of which Jamie would have two arms again, two hands, two sets of fingers…

Once cleared for the double transplant, he joined the list of those waiting for a donor. It would be over two years long.

“I thought about my daughters. They’d had to cope with so many changes,’ says Jamie. “I couldn’t die on them! But my immune system would have to be suppressed to stop my body rejecting the transplants…”

As Prof Kay told the makers of a documentary which airs tonight, telling the story of Jamie’s transplant, “The immune system fights infection, cancer and tumours. But Jamie has a real need and he’s a coper… with a very positive attitude.”

At stake was something deeply important and very human, a prize worth all the risks.

“Hands are what make us human,” says Prof Kay. “We do many things with them that other animals do not. We point, we gesticulate, we caress, we care…”

Jamie had no doubts in the end. He had to do it. “It was for a better life for us,” he says.

His bag was packed and ready. In the afternoon of March 29 last year, the call came. He had a donor.

He sat his daughters down. “I’ve got the call, girls,” he said simply.

Every day for the past two years he’d reminded them that it could be any day.

So there was no drama. Carla, was on hand to look after the girls. Jamie and hospital bag set off.

At 6am next morning a procedure that’s truly incredible began. It was expected to take 14 hours. Three hours in, the donor limbs arrived.

Carla sums up the emotion, “It is so remarkable that they would give this gift of limbs [of their child].”

Ten hours later, Jamie was out of surgery, his new arms in casts.

Coming round, he was on a high. “I think it must have been the drugs, a sort of walking dream but I saw my future and it was so bright and colourful. I was playing with the girls who were skipping around. It was euphoria.”

When he next came around there was only pain.

“But I could see fingers coming out of the bandages. The fingers felt like mine immediately.”

Tonight’s documentary captures the longed-for, magical first bundling of his daughters into those new arms.

Savannah and Bella take it all in their stride. Daddy is just Daddy. Always has been.

But for Jamie, their future is stronger now.

He is in awe of the gift he has been given, the selflessness that has made it possible.

Hands that are warm, that can pick up stray chips and discarded Hula Hoop crisps… Comfort his children or make them shriek with giggles… All little things that matter so much.

“I wanted to write to the donor’s family and put into words what they have done for me,” says Jamie. “I wanted to write it with my new hands.”

But being able to hold a pen is some way off - the transplanted hands will keep improving for the next four years or so.

Jamie’s gratitude couldn’t wait that long to be expressed.

“I have written an email instead,” he says. “Telling them how much this gift is changing my life. And what an amazing, kind and brave thing it was to give me their loved one’s limbs. I’m making good use of them.”

He’s also had the hands tattooed, one especially poignant.

“With a big stopwatch and the words ‘Nothing Is Forever’,” he explains. “A reminder that everything can change in a moment.

“I don’t ever want to forget that.”

● Saving Lives In Leeds starts tonight (Wednesday) at 9pm on BBC Two and BBC iPlayer.