In theory, action on child poverty in the United Kingdom is not one of those fine sentiments to which governments pay lip service.

The eradication of misery is not an aspiration. It's an obligation, enshrined in law.

The legislation in question is the Child Poverty Act 2010. It received its Royal Assent in the last days of Gordon Brown's administration. It contains a series of commitments that are, in fine theory, binding. Four targets to be met; strategies to be published; a commission to be established: and so forth.

In 2010, the basic point was simple: the British state would bind itself to the duty of ending child poverty by 2020/21. The Tories went along with the ambition, but quibbled, not for the first time, over definitions. They wanted targets mindful of poverty's "underlying causes". "Lack of money" was not top of the list.

Not long after coming to power, nevertheless, the Coalition turned the Act's Child Poverty Commission into the Social Mobility and Child Poverty Commission. A clue to Downing Street's thinking could be had from the renaming. The existence of poverty was located in the absence of social ladders. All could ascend - or so David Cameron would argue - if granted the opportunity.

It made no odds. Alan Milburn, a former Labour minister, accepted the oxymoronic title of mobility "czar". He set to work even as the Government insisted that children were being lifted from poverty and that welfare reforms had no relevance. Last October, Mr Milburn produced the first of the annual reports demanded by the Act. The precis was uncomplicated: the Government had not a hope in hell of meeting its obligation.

Another year, another Milburn report. Now the commission claims that the second decade of the 21st century will witness an increase in absolute poverty in the UK. This year's report says low pay, exclusion from the housing market and public spending cuts are taking their toll. Far from witnessing progress towards social mobility, Britain risks being "permanently divided" between rich and poor. It could all be filed under "Who'd have guessed?"

Mr Milburn's commission says political parties are being dishonest, both about poverty pay and the fact, now inevitable, that the state will fail in its 2020 obligation. In large part this is because cuts in benefits will - for how complicated is it? - drive the poorest deeper into poverty. The commission would like the Office for Budget Responsibility to judge a Chancellor's Budget choices by their effects on social mobility and the poor. It does not add "Fat chance".

Instead, Mr Milburn's report has caused a burst of creativity among the purveyors of fantasies. Carts are being slung in front of horses. Why not teach people to be better parents? Why not improve education and access to education? The Tories' Labour czar has gone at all of this with a will.

He mourns the fact that some children are in no state to enter education. Meanwhile, he deplores spending cuts. Equally, however, he wonders aloud why politicians won't "call out" parents who are not "effective". Poverty, it turns out, is the mark of a failed family. Strip out the mobility stuff and the parenting classes: the Victorians would have applauded the argument.

Stand it on its head, then. What matters most in this Britain? Education, or the means which allow educational advantage to be purchased? What's liable to have most effect on a child's life chances? Too few cuddles, as Mr Milburn has suggested ingeniously, or George Osborne's decision to freeze benefits for five million working families for two years while his opponents dither over the living wage?

Those who have most money do most for the education of their children. For them, the equation is never reversed. They are not asked to think less about cash until schooling has worked its magic. They understand the purchase price of social position. No one frets over the cuddling received by a child packed off to a public school. The civil servants who received that education - 55 per cent of them - know all of this.

Britain's poor don't have enough money. The elaborate rhetoric of mobility cannot disguise the meaning of simple words, or the effects of fundamental deprivation. The five million families about to be robbed by Mr Osborne require state help to make ends meet because the state will not insist on fair pay. And this explains bad parents, whose existence explains educational failure, and that explains rising child poverty? There are surreal fairy tales that make more sense.

Schooling matters. Those of us who squeezed through the narrow historical window when comprehensive education existed and student debt was a foreign phenomenon had that much drummed in. For a couple of decades, Britain tested ideas of egalitarianism and mobility. For a while, it worked. Perversely, it would even inspire the Blairite chant of "education, education, education". But politicians chose to forget the proper order for carts and horses. They decided it didn't much matter how education could be achieved.

So Mr Milburn is reduced to suggesting handy cuts for the Coalition as it steels itself to attack the rights of pensioners. He wants to pay teachers more to work in tougher schools. He'd like still more targets and a bit more haste, especially from his own party, in increasing the near-irrelevant minimum wage. When it comes to moral weight and economic heft, the former Health Minister is confused. Asking workers to wait until 2025 for the living wage is itself an acceptance of child poverty.

Mr Milburn knows that absence of money is, purely and simply, the definition of poverty. Yet palliatives, though he offers plenty, won't do in a society busy enshrining inequality. Scotland's attempts to ameliorate the problem have faltered in the last year, but any demands for the Holyrood parliament to do more should be backed with support for the full devolution of welfare if they are to stick. Scotland is not failing to do more because the SNP didn't make Mr Milburn's chosen cuts.

Beggar-thy-neighbour is an austerity game perfected by a Cabinet drawing its leadership from public schools. Did they benefit from lots of cuddling, then, or from unearned wealth? Did they learn about poverty from experience, or from a nuisance commitment devised by a previous government? Do they see the poor as Britain's shame, or as just another outlay to be trimmed while the children from 10 million households lack a future?

"The Scottish Government highlights welfare reform as the likely driver," says the report of Mr Milburn's commission, "but the same welfare policies have not caused a corresponding rise in poverty across the rest of the UK". That's not actually true. The report itself shows increases across these islands: that's the whole point, especially when Mr Osborne's reforms are being held up as a prime cause of misery.

Why should the children of the poor need to pin their hopes and dreams on things the wealthy take for granted? There is, as yet, no legal obligation on any government to address that ruinous state of affairs. Why not? Poverty, as the rich never care to grasp, does no-one any good.