Britain is facing a “crisis of fatherlessness” in which almost half of all children born today will not be living with both parents by the time they are 15, the new chief executive of the thinktank founded by Iain Duncan Smith has warned.

Andy Cook, who runs the Centre for Social Justice, which is chaired by the former cabinet minister, argued that regular contact with a father figure reduced criminal behaviour in children and boosted cognitive skills including reasoning and language development.

Cook claimed there was too much of a “throwaway culture” to parenting, adding: “Over the last 40 years, the meteoric rise in family breakdown has blighted the lives of the poorest children the most. The relationship children have with their father affects their self-esteem, how well they do at school, even whether they are able to form happy, long-lasting relationships as adults.”

Andy Cook of the Centre for Social Justice. Photograph: PR

The Observer can reveal that tackling family breakdown was going to be at the heart of David Cameron’s “life chances strategy”, which was to be released as his government’s flagship policy within days of June’s EU referendum result. But after taking over as prime minister, Theresa May ditched the proposals, which some see as controversial because they include a value judgment and risk stigmatising single parents.

However, sources have told the Observer that a new social justice green paper – due to be published within weeks – will have family stability at its heart. The plans will focus on helping parents to develop a strong working relationship, but they will stress the need to target efforts not only on couples but also on those who have separated.

Cook said it was inevitable that relationships would not always work out, but argued that a culture shift could reduce the prevalence of family breakdown, and stressed the importance of parenting once couples had separated. “We need a societal shift in perspective from regarding fathers as a dispensable extra to recognising their value as a crucial pillar in a child’s life,” he said.

He said he first started a small charity after meeting two 17-year-olds, Ash and Terry, on an estate in Loughborough, Leicestershire, with no prospect of employment. Cook was taken aback by their lack of life chances, claiming “if it is happening in leafy Loughborough, what is happening in Leeds or London?” The “lads” each had five or six siblings, and all with different fathers, he said.

He argued that it was important to help people to be resilient as relationships go through ups and down, saying “there’s quite a throwaway culture; if things aren’t working, people try something new. We are trying to find a way to support people like Ash and Terry to find a relationship and try to stick with it.”

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Cook said policy ought to be focused on longer-term thinking, and emphasising the potential impact on children of troubled relationships, stressing the disproportionate effect on the poorest. His thinktank’s figures show that by the age of five 48% of children in low-income families are not living with both parents, compared with 16% of children in middle- to higher-income families.

He said his work would also focus on four other factors that contributed to poverty: educational failure, worklessness, problem debt and addiction. Looking only at income levels skewed policy, he added. Despite controversy in the education sector about the growth of grammar schools, allowed by May in one of her first acts as prime minister, Cook argued that there was evidence they could be successful if headteachers tried to find the most talented children from poorer families.

The work on Cameron’s strategy was led by a former chief executive of the Centre for Social Justice, Christian Guy, who became the PM’s poverty adviser. He said the hope of the previous strategy was to “start a parenting revolution – for too long politicians looked away as family instability and poor child development blighted lives in the poorest neighbourhoods”.

“Parents want what’s best for their children, but great advice tends to be the preserve of the better off. This has to change if we want to see children starting school ready to learn, to communicate and forming healthy relationships.”

Guy said that supporting parenting should be a top priority for those trying to tackle poverty. “Whatever Theresa May calls her strategy, stronger parenting should be at its heart,” he added.