If you were a financier, and someone approached you and whispered, pssst, wanna invest £191 billion for a return of £269 billion in ten years, you might break stride and roll a quizzical eye.

If the same person then warned you that if you didn’t invest, you would be personally liable for outgoings of nearly £4 trillion over the next 20 years, you might just start listening.

These figures are remarkable — not just because of their vast size, but because they represent the first, independent, hard-nosed costings surrounding social problems in Britain, and the undeniable financial case for doing things differently from how we do them now.

An impressive report, published yesterday by the charity Action for Children and the New Economics Foundation provides a comprehensive cost-analysis of crime, mental ill health, drug abuse, family breakdown and violence. Let’s set aside for now the unquantifiable cost in human misery in the statistics: here, in rows of raw zeros, in language that bean-counters understand, is what the taxpayer pays for other people’s lives going wrong.

And here too, for the first time, is the powerful economic case for reconfiguring what we do: for substituting the present sticking-plaster system of children’s services — waiting until infants are at risk, then patching them up until the next time — with a preventive approach. And guess what, the conclusion is that by doing so, we could reduce the bill to society by those aforementioned trillions.

At present, the UK forks out £161.31 billion annually on social problems — from special schools to social workers to foster parents to jailing criminals — all of which begin in childhood and almost all end in prison. We have had Baby P, we have had Edlington; this week’s incident, should you need reminding, is the case of three brothers, aged 8, 11 and 12, questioned over the alleged sexual attack on and torture of three other children in a Bristol park.

Everyone involved in dealing with this tragic parallel world to ours knows that the system isn’t working. Things are deteriorating. Professionals and politicians know intuitively that swifter, effective intervention in troubled families will achieve better outcomes. As Clare Tickell, the chief executive of Action for Children, puts it: “Everyone understand that. It is a no-brainer.”

But until now, no one had the ammunition to prove the negative — to show that the absence of intervention costs so much.

The report, Backing the Future, does the maths for us. It suggests that over the period from 2010 to 2020, sufficient targeted interventions in children’s lives would cost an extra £191 billion, while the total saving would be £460 billion. If this spending were funded through a bond scheme, the net return on this investment would be £269 billion.

Within nine years, it is calculated that the cumulative savings of the new approach would break even with the cumulative costs. In the decade 2020-30 a second wave of help, involving new universal childcare and funded parental leave, as proved elsewhere in Europe, would kick in.

Over 20 years the whole package would bring net returns to the UK economy totalling £486 billion — roughly five times the current annual budget of the health service.

The costs are of course substantial: additional spending of £620 billion over 20 years, which the report suggests could be raised by issues of bonds. This roughly equates to doubling current GDP expenditure on children and families (3.5 per cent to 7 per cent). By 2030, however, the report forecasts, the percentage will have returned to where it is now. What will have changed is the composition of spending, with a focus on prevention, in line with the European countries with the fewest social problems.

The result, the report suggests, will be improved child wellbeing, a reduction in social problems, benefits to communities and savings to the economy. Happier children, less violence, less vandalism and drug abuse and fewer people in prison. Every year that the investment is not made, by contrast, costs will continue to grow and the bill for maintaining the status quo until 2030 is £4 trillion — without addressing the root causes of the problems.

The beauty of Action for Children is that it cannot be accused of being out of touch, as the many Times readers who contributed to its admirable frontline work last Christmas will testify. A Social Return on Investment analysis of its projects, teaching parenting skills, helping families in crisis and suchlike, shows that for every £1 invested annually in its targeted services, society benefits by between £7.60 and £9.20. (The return is probably much greater: to ensure that they were not overclaiming, the researchers halved the impact of the interventions.) Financiers, sceptics, bleeding hearts and all, there we have it: a body of evidence that demands not that the tanker needs turning round but that it be shifted in a different direction. Of course the extra money, at a time when everyone is talking about cuts, is politically difficult, but the intellectual and economic argument for taking a long view could not be more convincing.

Nor, I suggest, could the electoral argument. Given the strength of public feeling about recent tragedies, any party that seeks to rescue children — to rescue them properly — might just find itself on to an irresistible winner.

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