Geoff and Ben Beattie are not the world's most obvious father and son. Geoff, a celebrity academic best known as the Big Brother psychologist, is short and muscular, with a California tan and the cheery, eager-to-please, fast-talking demeanour of a TV personality. Ben is tall, slender and reserved, and works in a bank.

They are so different that people occasionally mistake them for a gay couple, particularly when demonstrative Geoff lavishes his son with kisses.

Geoff and Ben share one important attribute: they are both runners. This is not simply a passion passed from father to son like a baton in a relay – it is a shared state of being. And running has brought them together again after nearly a decade in which Ben refused to speak to the father he could not bear to be around.

Geoff began running as a child growing up in what was called the "murder triangle" in north Belfast. When he ran across the peace line – betraying the fact that he was a Protestant – gangs would hurl bricks at him.

Told by a teacher he came from the gutter and would end up back there, this driven, ambitious Ulsterman set about proving them wrong: after studying at Cambridge University, he became a lecturer at Sheffield. By day, he taught psychology; by night, he hung out with bare-knuckle fighters, burglars and call girls, writing features about the underbelly of northern England under Margaret Thatcher for the Guardian.

All the time, Geoff ran. What is the longest period he has gone without a run? "I run every day," he replies, as if it's a silly question, when I meet father and son in Manchester. "I don't do rest days. I have to do it."

In Chasing Lost Times, the running memoir Geoff has written with Ben, they explain all the reasons they run. Mostly, it keeps them happy, balanced, on track. "To me running feels like some sort of self-correction process," writes Geoff. "It pulls me back to the real me."

Other reasons to run include connecting with childhood (Geoff), being with Dad (Ben), and less positive compulsions including guilt, fear, competitiveness and vanity. But Ben, who is 29, returned to running six years ago for a specific, vengeful reason: he wanted to take something away from his dad. "I could never take away his academic qualifications or his money but I could take away his achievements in running," he writes. The eldest son was desperate to beat his father.

Running was a battleground when Ben was growing up in their home in a converted asylum on the moors above Sheffield. Family meals were delayed so Geoff could run. Ben wanted to stay in the warm but his dad would beg him to come, and then speed off, leaving his son shivering or lost on the moors. One time, Ben deliberately fell into a snowdrift in the hope it would halt their run; Geoff ploughed on.

Geoff was putting more than running ahead of his three children with Carol, his teenage sweetheart from Belfast, who also became a psychologist. One day, trying to catch a train, Carol fell on to the track and slipped under the wheels. Her arm had to be amputated. After the accident, Geoff had his first of many affairs.

When Ben was 17, he discovered the secret at the heart of their family. His father's frequent absences were not just philandering. Geoff had a second family – two children with a long-term girlfriend. Ben remembers his younger brother asking where Dad went on Christmas Day. Carol knew but, according to Geoff, asked him not to tell the children.

"From my point of view it's a completely no-win situation because you're leaving one set of kids and they are feeling awful and you're going to another set of kids and they are feeling awful," he says. "You're just stuck. It's a ludicrous position to get into but it happens. I'm sure I'm not the first. It was just an awful, awful situation."

Ben was furious about how his father treated his mother. "I've got so much admiration for her – I just thought: why?" he says. Geoff moved to Manchester, where he took a new job, but continued to spend weekends at the family home. Ben avoided his dad. If Geoff entered a room, Ben left. For a decade they never spent any time alone together. Geoff feared – rightly – that his eldest son despised him.

"My goal was to be nothing like him at all," says Ben. He stopped running, dropped out of university and became a bar manager. Increasingly unhappy, he found himself living near his dad again. They met for a few tentative lunches and Ben decided to run a 10km race and beat his dad. Unfit from drinking and smoking, he was overtaken by his dad with 2km to go.

Geoff laughs uproariously at the memory. Is this Competitive Dad delight? "No, no, no, no, no," chuckles Geoff. "It's only funny because he is so good now. The weird thing is that I don't feel that competitive about running at all. Ben's mum is very competitive; he's really competitive."

"I think you are competitive," says Ben softly.

Originally they intended the book to cover the psychology of running (Geoff's field) and the physical challenge (Ben's bit). But Ben, who now runs twice a day and more than 100 miles a week, found he couldn't write about his return to running without explaining why.

Geoff is as open and self-reflective as any psychologist but it was only Ben's challenge "to come clean" that made Geoff decide to write about "this other life", as he calls it. "Ben wasn't happy talking about it, so we had boxed it off. Through the book we opened a conduit through which we could say how we felt," says Geoff.

Even then, he admits, "I glide a little bit over stuff"; when Ben read a draft chapter that included a sentence that said perhaps Geoff "had his reasons" for the affairs, he exploded and told his dad he had to face up to what he had done.

For the first time, through the book, Ben told his dad he had almost hated him. "In some senses it's reassuring to hear that," admits Geoff. "I seemed to make Ben very angry because I have this way of going through life – it's just a persona to get through life – but it really pisses Ben off. Is that true?"

"Yeah. He's quite a tiring person to be around," says Ben gently.

Chasing Lost Times certainly illuminates the emotional lives of a father and son. There is one perspective missing, however: the mother and wife. One day nearly 10 years ago, Carol took an injured Geoff to the gym so he could exercise. She was so bored that she stepped on to a treadmill. She now races and regularly wins her categories.

With Geoff living in Manchester and Carol in Sheffield, I assume they are divorced. "No, we're still married," says Geoff. "She's my running partner on a Sunday. So we go to races most weekends. We spend a lot of time together." Are they still together or are they single? "Who knows? You tell me," says Geoff lightly.

"It's complicated," says Ben.

"It's complicated," nods Geoff.

One of the most searingly honest passages in the book is Geoff's account of a race last summer when he spotted Carol not far behind him. His one goal, he admits, was to increase his distance from her. "I pictured Carol back in university, trailing along after me on the way into the department," he wrote. "She had followed me to England, she had followed me into psychology and here she was following me in the mud in the middle of nowhere in the pouring rain."

Carol is "ludicrously competitive", says Geoff now. Later, with less ebullience, he admits she is "not a fan" of the book and was "nervous" about its very personal revelations.

"There's obviously a lot in it that's difficult for us to read, and it's difficult for her to read," says Ben.

Geoff admits that Carol is "absolutely core" to their story. "You could not have more admiration for a woman – I don't want to get too emotional," he says, as his eyes redden. "She never makes any excuses about life. She never did. She brought up three kids. One arm. She is a fucking amazing woman. I've never changed my views on that. Unfortunately I did what I did, and for complicated reasons."

Geoff's explanation is that he was mourning the death of his brother, and his father, who died when he was 13, and "clearly needed someone to talk to". He didn't talk to Carol; he would have been "ashamed" to offload on her when she was dealing with the loss of a limb and so he found people to talk to through the affairs. "Honest to God, I'm saying that was my mechanism. It sounds ..." he tails off. "But she is a remarkable woman, there is no question about that, and the kids grew up with a remarkable mother and she is remarkable with me, actually, still."

What sort of father does Geoff think he has been? Unusually, there is a long pause. "When Ben was growing up, I was so aware there were a million and one things I wasn't doing – ferrying the kids around. Carol did all that stuff. In that sense, I was an awful father. But I have certain qualities. I don't give up – Carol always described me as irrepressible – I can deal with major stuff. If part of being a good father is passing that stuff on to my kids then that's what I've done, which is positive."

Geoff hoped the book would bring about a full reconciliation with Ben but by its end admits they are not there yet. Where would they put their relationship now? "On a 10-point scale?" volunteers Geoff.

"Eight," says Ben.

"That sounds about right," chuckles Geoff. "Before it was about two." He looks across, a little anxiously, at Ben. "It was really bad."

Is the book Geoff asking for forgiveness from his eldest son? "I want to come across as a carefree guy who doesn't give a shit but, actually, I come from an Ulster Protestant background. I have terrible, terrible guilt. I suppose a book like this is an attempt to say, this is what happened, this is my only explanation. Is it a plea for forgiveness? I would say it was. I would say it had to be."

Has he asked Carol for forgiveness? There is another long pause. "I haven't, no," he halts again. "I've said to her a million times, 'I'm sorry, I'm sorry things happened like this, I'm sorry I wasn't different.' But I don't think that's quite the same really. I suppose I can't say, 'Can you forgive me?' because I'd be too frightened of her replying, 'No, I can't.'"

The three of them, Geoff, Carol and Ben, go running together. "I'm sure people think it's strange when the three of us rock up at a race," says Ben. After knocking more than 10 minutes off his dad's best ever (1hr 26min) half-marathon time, Ben hopes to run a half-marathon in less than 70 minutes. Geoff, fresh from winning three prizes at races in California, hopes to set a new personal best time in the 10km. Both men worry about Carol, whose own pursuit of records has led her to collapse at several recent events.

Ben is more willing these days to recognise what he shares with his dad. "Apart from a nose, that dedication, that single-mindedness and that willingness to prioritise one thing. For me it's running. For you," he says, turning to his dad, "it's your career over everything else."

Ben has also become more tolerant of his father since he's made his own mistakes. "I was quite a judgmental child. I thought everything should be a certain way," he says. "As I've got older I've realised you can get into situations not of your own doing. Things happen, things spiral."

Has Ben forgiven his father? Now it's his turn to pause. "I probably have but at the same time there's this nagging thought at the back of my mind – it's not me that needs to forgive. There are other people and they are still angry, and I still hold a little bit of resentment on their behalf."

• Chasing Lost Times. A Father and Son Reconciled Through Running by Geoff Beattie and Ben Beattie is published by Mainstream, priced £11.99. To order a copy for £9.59, including free UK pp, go to guardian.co.uk/bookshop or call 0330 333 6846

Book extract: 'I was close to hating my dad – he made me so angry'

Ben: Looking back now, I cannot ever imagine hating my dad but there was a time when I must have come close. I didn't want to see him or speak to him. I didn't even like to hear his name mentioned.

I would fantasise about a time when I would be stronger and I could hurt him, he made me so angry.

My resentment didn't centre on myself or even my brother and sister but on the treatment of my mum. In my mind, she could and can do no wrong and didn't deserve such rotten treatment and disrespect. So I would imagine a time when I would be able to beat him – literally.

In hindsight, maybe becoming a better runner than him was my way to prove my manhood and at the same time take something away from him. I could never take away his academic qualifications or his money but I could take away his achievements in running; achievements that he was incredibly proud of.

After beating my dad in a head-to-head race, the next obvious target to focus on was my dad's personal bests. This drove me forward.

Geoff: I had never been with anybody else but after [Carol's] accident I had an affair. It wasn't difficult; the girl made all the approaches and she knew that I was married. We were both in our early to mid-20s.

In retrospect, I think that the sex for me was a mechanism to get close enough to someone to open up to them. This must be one of the best excuses ever, laughable to some, but quite true; at least, that's how it felt. Today, I can't remember the sex, or any excitement or any real desire, but I can remember lying in a bed with dank, cheap, blue sheets, with little bits of silver jewellery on the sideboard, and talking about Bill and Carol and my mother, and fragments of my life in Belfast, and feeling much better for it. Very guilty but better inside. I'm not, after all, the kind of person who could go to a counsellor or a psychologist; they'd probably know me for a start.

I can remember the Human League playing in the background, something about a crow and a baby having an affair. "A new band from Sheffield," she explained. "I know the singer."

The whole thing was also, of course, unforgivable and Carol never really did forgive me when she found out, which she did almost immediately. She said that at one level we were finished, but I felt she needed me and I certainly needed her. We thought a family would bring us closer together; soon afterwards our wonderful daughter Zoe was born and Carol's life changed dramatically again, but this time for the better.

I felt I could never leave her; I loved her too much, and I respected her more than anybody in the world. I still do, but there are many other layers of emotion in there as well now, not surprisingly.

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