Imagine a policy that makes a very small number of poor families significantly worse off, but which doesn’t address any of the underlying problems afflicting them.

And imagine, too, that this policy saves the taxpayer virtually nothing, while feeding a pernicious myth that the UK’s welfare system is a giant racket for the workshy.

Does that sound like something a sensible and humane government should be doing?

Corbyn tells Theresa May to watch I, Daniel Blake to understand benefits system

This week the benefit cap was forced down onto the heads of tens of thousands of families by the Government. In 2010 George Osborne came up with the idea of restricting the total amount in state benefits a single workless household could claim to £26,000 – arguing no family should be able to receive more in benefits than an average full-time worker makes in wages.

As of this week the cap has been reduced to £23,000 in London and £20,000 elsewhere. This will increase the number of families impacted from 20,000 to 88,000; still not a big number in the context of the UK’s 26 million households.

The workless families affected by the first stage of the cut had two principal characteristics: relatively large numbers of children, meaning they were eligible for higher than average child benefit payments, and high housing costs, meaning they received higher than average housing benefits.

Almost half lived in London, where rents are particularly elevated due to a chronic shortage of housing and the housing benefit bill is correspondingly massive.

The Work and Pensions Secretary Damian Green has heralded the first phase of the cap as a “real success” and asserted that it encouraged affected families into the workplace.

But the Institute for Fiscal Studies reckons only 5 per cent of those households hit moved into work specifically because of the cap, which hardly suggests an effective welfare-to-work policy.

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An even smaller proportion moved into smaller homes to cut their housing benefit bill. The majority of those affected did not start working and did not move house but merely absorbed the pain of the cut and became significantly poorer as a result. And this pain will now intensify.

Those households newly affected by the cap will lose an average of £2,000 a year in benefits. Those already hit will lose a further £3,000 to £6,000 a year, depending on where in the country they live. Could you afford to lose £3,000 a year? And how much will that punishment benefit taxpayers?

The Treasury estimates a saving of £100m a year, which is less than a tenth of one per cent of the total UK welfare bill.

And it’s doubtful even this will be recouped. Many councils responded to the first phase of the cap by subsidising affected families with Discretionary Housing Payments, offsetting almost 40 per cent of the original £65m saving.

What would a sensible policy designed to assist families with large numbers of children into work and to cut the overall benefits bill look like? To ask the question is to realise instantly that the benefit cap is not a sensible policy.

It does not address the underlying reasons why a small minority of families receive outsize benefits payments, primarily the fact that rents have soared due to a chronic shortage of new housing supply.

If the Government wants to reduce the housing benefits of families (and not just the payments to workless families) it needs to build much more social housing.

On the child benefit front, the policy is equally wrongheaded. Government welfare policy is specifically designed to target children living in poverty, which is why payments rise when low-income families have more children. Placing a hard cap on benefit payments to those with large families just pushes in the other direction, undermining the first policy.

If the Government really feels it is justified to reduce payments to families that have large numbers of children – and is prepared to defend the increase in child poverty – it should do this directly, rather than achieving it through an arbitrary cap.

Yet polling shows that benefits cap is popular with the public – indeed it has been one of the Government’s most popular single policies in recent years. Why is that?

Almost certainly because the smiling workless family with large numbers of children supposedly living lives of “luxury” on benefits has been a staple of the right-wing tabloid press for decades – cementing the false public impression that Government welfare payments primarily flow to the feckless and workshy.

In reality, a very large share of the working-age benefits bill is payments to low-income families who are working or who are disabled, in the form of tax credits and housing benefit – one of the reasons Mr Osborne’s framing of the issue as a comparison between average full-time wages and a household’s benefits payments was so toxically misleading.