Penelope Leach has a request. Imagine if you will, she says, a Britain in the throes of a terrible medical emergency; an epidemic that targets the nation's children, leaving half of them missing a limb by the age of 16. It would, without doubt, be devastating. "People would talk about nothing else," she says. The media would be overflowing with information and advice on how to tackle it; all possible resources would be channelled into dealing with it. As a society, we would focus on how to mitigate its effects and how to stop it causing such massive damage.

Leach, Britain's leading parenting guru – her comprehensive classic Your Baby and Child has been an international bestseller for almost 40 years – wants us to imagine this because, she says, there is an epidemic. It has hit more than half of all children by the age of 16 and the damage it causes – though not visible, as a lost limb would be – is just as life-changing and far-reaching. The epidemic is relationship breakup (not marriage breakup because, as she points out, not all parents are married in the first place) and its victims are the children of those relationships.

Even babies can be harmed, Leach says, if they are shuttled around and taken from their primary caregiver. "We can argue about all sorts of things around the edges, but we can't argue about the damage it does," she says. "Divorce or separation will always be bad for children – there's no getting away from it. It ranges from disruptive and sad to tragic. What's best for children is if their parents love one another for ever … but there are always lots of things that you can't get perfect for your children."

The problem, and the reason Leach's latest book is devoted to the topic, is that she thinks we are failing to do in divorce what we manage in other areas – to do as well as we possibly can by children despite not being able to give them the best. In other words, we can do divorce better. In fact, says Leach, we must do divorce better. "The numbers are going through the roof, but we're not handling it, or dealing with it, any more successfully at all. Break-up is seen as primarily adults' business, but it's just as much about children's lives," she says.

"Children are being used as weapons in the marital war when actually they are its victims."

Leach's fear was that with this book she would be accused of being anti-divorce, in much the same way that her detractors have long accused her of being anti-childcare and in favour of mothers staying at home. In fact, in the last few days newspapers have pilloried her for being anti-fathers, an accusation that has horrified her. "My new book is pro fathers, not anti them," she says indignantly. "The main reason I wrote it was to help parents to work together after marriage break-up, and a big part of that is so fathers get the role they deserve and their children need."

She does indeed say that, in most cases, it's best if under-fours who are living with their mothers don't go to stay overnight with their fathers: it can undermine their security, she says, could make them more irritable, and might interfere with their social development. But headlines about "fathers' fury" have hurt her deeply. "In the vast majority of cases, it's the mother who is the primary attachment figure – young babies need a primary caregiver and being separated from that figure can cause them problems. If a father was the primary caregiver I'd say the baby shouldn't be staying overnight with the mother.

"But I believe fathers are just as important to a child's life as mothers, though the timing is different. They tend to come into their own in the second year, rather than at birth, and children who have a close relationship with their fathers do better through life in every way."

The incidence of divorce has gone up exponentially since the early 20th century. In 1885, there were 300 divorces in England and Wales. A century later, the figure was 160,000. In the UK today, around 42% of marriages end in divorce and the peak for splits is between the fourth and eighth years, when couples are most likely to have young children. In any case, as Leach also points out, the Office of National Statistics predicts that by 2016 more than half of all babies will be born outside marriage – and breakdowns in cohabiting relationships go below the radar, so the true extent of the effect of a parental split on children today is difficult to quantify and figures almost certainly underestimate it.

Leach tells a story about asking a 13-year-old girl whose parents had separated if it was something she could share with friends at school. "She looked at me in an amazed way, and said, actually, there are only two people in my class whose parents are still together."

So she is not, she insists, on a mission to keep parents together: she believes that once a relationship has reached its end-point, nothing will save it. She is often asked whether a couple should stay together for the sake of the children. "My reply is, it has to be about what it would cost you to do that. It's not about self-sacrifice. It couldn't be right for me if it wasn't right for my child."

That philosophy is the kernel of Leach's thinking: for her, what is right for the parent is right for the child. She believes, too, that we have underestimated the effects of divorce on two groups of children: the very young and the almost-adult. "We tend to focus on the four year old who's wetting his bed, or the eight year old who is throwing chairs round the classroom. But there's increasing evidence about how affected babies are by what happens in even their earliest months and, equally, it's wrong to think that older adolescents won't be hit hard by divorce. It can blow apart their whole personal history: all those summer holidays together, all those seemingly happy family Christmases, have been falsified in one swoop."

Penelope Leach: 'My parents got it very wrong. They split up when I was 10, and it was a very difficult time for me.' Photograph: Sarah Lee for the Guardian

The mode of parenting she espouses is very much the mode of parenting she practised herself. Now 76, she was an ever present mother when her son and daughter were growing up (she raised them without a nanny, she says, just for the record, juggling their care alongside her academic work as a psychologist and then her writing).

Today, she is a hands-on grandmother of six living in Sussex, having moved from London, where she had lived all her life, after the death of her husband, Gerald Leach, a science writer and environmentalist, 10 years ago. Theirs was a long and happy marriage, so she is conscious of not having had to deal at first hand with splitting up. "Am I saying everything I'm suggesting is easy? No. Am I saying I could have done it? Fortunately, I didn't have to, but I hope I would have done it right if it had been necessary."

But it turns out that she does have personal experience of divorce, and from the very viewpoint she is urging all of us to take: the child's. Her parents, the novelist Nigel Balchin and his wife, Elisabeth, went through what sounds like a very messy divorce after a partner-swapping arrangement with the artist Michael Ayrton and his wife, Joan. "My parents got it very wrong," says Leach. "They split up when I was 10 and it was a very difficult time for me – I think I got through it partly by focusing on looking after my younger sister, who was three at the time. But I think that's one of the reasons all this interests me so much, and I think it's why I've always been so drawn to the study of attachment."

Leach was very close to her mother, she says, and quite distant from her father. "But I did have a warm relationship with my stepfather [Ayrton]. He made my mother laugh; people say children only think of themselves, but that sold him to me." In her book, she tells the story of an 11-year-old girl, the middle child of three, sent to boarding school "because her furious father couldn't, and didn't pretend he wanted to, look after her and he would not allow her to live with her mother and her mother's lover [her future stepfather]. Her older sister escaped to drama school, her much younger sister was allowed to stay with mum. This child felt herself to be out of sight and out of mind." It sounds remarkably like Leach's own tale: when prompted, she admits that yes, the child she is quoting is herself. "I felt I'd vanished," the unnamed child says in the book.

How, then, did she survive the trauma of all that? She pauses. "Did I survive? We never know, do we, because you never know how you would have been. Early trauma can leave people sensitive to stress later on in their life, and I think I'm someone who demonstrates that. I'm not a laid-back sort of person."

So what is the right way to divorce? What is the better way forward that eludes millions of separated parents, and that so eluded Leach's parents in the 1950s? The answer is what their daughter calls "mutual parenting": the secret, she says, is that parents who no longer love each other and would do anything rather than even be in the same room, must still be prepared to engage in mutual parenting.

Such parents must separate their sexual relationship from their parenting relationship; they may have decided to put the former behind them, but they must keep the latter in mind. "You have to put your children's needs, not your own, at the very heart of it all: so it's not about getting revenge or working out your animosity, it's about remembering that your former partner is the very best father or mother for your child. That's why I can't understand why people want to airbrush their former partner out of the equation because their presence is really important for the child's future."

She doesn't, she says, want to make assumptions about this, but the reality is that 92% of resident parents in single-parent families are mothers, so it's usually fathers who disappear; yet the research shows more and more how important fathers are in children's lives. "The role of the father, from the earliest days, is so much a factor in what's going to happen later on in the child's life," she says. Not being around doesn't make a dad any less important, either.

It's about helping parents who have split up to continue – or perhaps in some cases, to begin – to be as generous and enabling with their ex-partner as a parent, even though they can no longer be generous and enabling with them as a spouse. "So if you agree to go to your child's school concert together, and your ex is late, don't immediately jump to the worst conclusion and bad-mouth him in front of your child. Don't say 'He's forgotten'. Say 'He's been held up, he'll be here as soon as he can'. Try to see him in the best light as a parent, even if you can't see him in the best light in other ways."

The bottom line, says Leach, is this: parents matter and the more research psychologists and neuroscientists do, the more we realise that they matter even more than we knew, that their influence is even greater than we once imagined, and that it continues for even longer than we thought. Monogamous long-term relationships may be on the wane, but a full realisation of the importance of parenting is on the up. Says Leach: "If you can no longer be a wife, a husband or a partner, you must remember this: you will always and for ever be a mother or a father."