The Consumer Prices Index is a strange sort of political toy.

It is crude, arguably deceptive, and at best no better than a partial snapshot of daily reality. It comes nowhere close to the whole story, yet governments swear by this one piece of statistical holy writ.

How can they or anyone else rely on a guide to the cost of living that takes no account of housing? The crude answer is simple enough: if interest rates control inflation, you can't honestly include mortgage interest charges in your calculations. But if you risk losing your home when a housing bubble bursts, or when the Bank of England decides rates have been too low for too long, that's scant comfort. It also fails to explain why the Consumer Prices Index (CPI) takes no account of council tax.

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What is this "cost of living" in any case? Intuitively we know that your spending and my spending will not be identical, that outgoings for young parents and the bills faced by a pensioner are very different things. But there's the CPI: a monthly calculation of allegedly average price changes across a "basket" of 700 goods and services according to data gathered from 120,000 retail outlets.

You could call it quirky. Last year, for example, the Office for National Statistics (ONS) decided there was no longer a need to include champagne in its virtual basket. White rum was preferred, the better to reflect the drinking habits of younger people, so it was said. Does that feel like your reality? How about "continental meats", newly included, or digital TV recorders? If you're still buying round lettuces, on the other hand, your purchases are no longer of interest to the ONS.

There is a serious side to all of this. Last year, the Centre for Economics and Business Research calculated that the CPI had gone up by 17.7% between 2007 and 2012, but the cost of food and non-alcoholic drinks had increased by 28.2%. Most of us probably realised as much. Nevertheless, while the richest 10% of the population spent just 4.2% of their gross income on such items, the poorest spent 23.8%. If poverty is relative, so is the cost of living.

These are hard times. Economic survival is, for millions, the only political issue to matter. Politicians have taken note. Ed Miliband and Labour call it a "cost of living crisis" and link it to another fact of austerity life: for the majority, wages have been stagnant or falling. As Mr Miliband has said repeatedly, the richest have been doing very well indeed; the rest are "working harder for longer for less".

Given that this is a fact of life, and one only too well understood by voters, David Cameron's Government has struggled to respond. Claims that the economy is growing once again might impress City economists, but few others. To put it no higher, modest GDP numbers are not helping the majority to pay the bills. If Mr Cameron cannot manage reality after almost four years in government, therefore, he must attempt to manage perceptions.

Yesterday his administration made a bold, even brazen, effort. In the year to April 2013, it was announced, CPI inflation was 2.4%. For all but the richest 10%, meanwhile, take-home pay went up by 2.5%. So 0.1% of a cheer for that. Faced with such a gift, you might say: "Don't spend it all in one shop." But you might also notice a couple of things.

First, this "rise in living standards" is only real thanks to cuts in income tax and national insurance. Average wage levels did not, of themselves, increase. In effect, the Government has subsidised stagnant pay rates. But it has also been hammering away merrily, simultaneously, at social security and other benefits designed to support incomes. Take those cuts into account, as Labour was quick to point out, and the crisis remains. Most are worse off than before.

George Osborne and Iain Duncan Smith could probably tell you why it was an act of economic genius to attack incomes by chopping "welfare" while the economy was in the tank. Few others would have the audacity. The Coalition has indulged itself with an opportunistic experiment to shrink the state at the expense of all those "hard-working families". Those households have meanwhile been made to foot the bill for the bankers even as wealth has continued to flow to the protected rich. How is that justified?

The meagre answer from Mr Cameron is statistical hokum and still another plea for patience. Even in Treasury terms, it doesn't add up. Yesterday, Paul Johnson, director of the Institute for Fiscal Studies said, bluntly: "If the recovery takes off and continues as expected, people will start to see their incomes rising by 2015 ... But they will be well below where they were six or seven years ago".

Even this slight degree of progress is "average"; much of it is marginal. Better than 60% of people in the UK receive some part of their income from the state. The greatest number of those are pensioners who are, for straightforward political reasons (they vote) safe enough for now. For the rest, there is not even the pretence of justice while Mr Duncan Smith spins webs of factually dubious populism and rank prejudice.

In a speech on Thursday the Work and Pensions Secretary was still presenting cuts to basic income as liberation from "entrapment". He had the nerve, indeed, to compare himself with those who ended the slave trade, as though the victimisation of the poor was the most moral act conceivable to his species of Conservative. He seized on a disreputable Channel 4 parody of journalism to once again justify persecution. But he failed to solve his leader's political problem.

Reality persists. Mr Cameron's manipulation of earnings figures ranks with his Government's boasts over unemployment. The raw total has declined: no argument. More are "in work": perfectly true. But what's the quality of those new jobs? How's the pay, the security, the hours for those who need full-time employment and want, contrary to Mr Duncan Smith, to work? What impact has a drop in unemployment had on in-work poverty while the minister hacks at benefits? Precious little. And this is no secret.

Like the CPI, the joblessness numbers amount to a fiction. They are part of the attempt to disguise the heart of the matter. The real crisis in the western world, the crisis Mr Miliband struggles to name, is in essence a matter of fair pay. This week we heard from two Stirling academics, David Comerford and David Eiser, arguing that an independent Scotland could not deal with inequality through the tax and benefits systems alone. Perhaps so. But decent wages, justice in employment, were the parts missed in the jigsaw.

Mr Miliband has edged towards that conclusion in his usual nervous way. Mr Cameron meanwhile could not reach an honest view unless he sacked his Work and Pensions Secretary, his Chancellor and, logically, himself. Statistical sleight of hand does not fool even half of the people half of the time. Until the cost of living is balanced by decent rewards for work, Britain is going nowhere.