David Cameron's pledge to cut the benefit cap from £26,000 to £23,000 if the Tories win the next election is one of the least surprising of the Conservative conference. Cabinet ministers such as George Osborne and Iain Duncan Smith have long signalled that they believe the cap, which ranks as one of the coalition's most popular policies, should be significantly reduced. (A YouGov poll published earlier this year found that 79 per cent of people, including 71 per cent of Labour voters, support the cap, with just 12 per cent opposed.)

It is undeniably good politics. Most voters regard a cap of £26,000 as unacceptably high and the move draws a sharp new dividing line with Labour. By pledging to use the money saved to fund apprenticeships, Cameron sends out the message that the Tories support work, not welfare. But while politically astute, the policy is profoundly flawed.

Rather than tackling the causes of high welfare spending, such as extortionate rents and insecure work, the cap places a crude and arbitrary limit on benefits. It applies regardless of family size, breaking the link between need and support. As a result, most out-of-work families with four children and all those with five or more will be pushed into poverty (defined as having an income below 60 per cent of the median income for families of a similar size).

Iain Duncan Smith has claimed that "[at] £26,000 a year it's very difficult to believe that families will be plunged into poverty" but his own department’s figures show that the poverty threshold for a non-working family with four children, at least two of whom are over 14, is £26,566 - £566 above the cap. The government's Impact Assessment found that 52 per cent of those families affected have four or more children. With the reduction of the cap to £23,000, even more would be left in poverty. In no sense, as Cameron suggested on The Andrew Marr Show this morning, is it "too loose".

While a childless couple who have never worked are able to claim benefits as before (provided they do not exceed the cap), a large family that falls on hard times suffers a dramatic loss of income. It was this that led the House of Lords to vote in favour of an amendment by Church of England bishops to exclude child benefit from the cap (which would halve the number of families affected) but the defeat was subsequently overturned by the government in the Commons.

The policy has been sold as an essential deficit reduction measure. But in practice, the savings are likely to be meagre, or even non-existent. A study of the cap's effects in Haringey, one of the boroughs where it was piloted, found that while the measure was saving the council £60,000 a week after, it was costing nearly as much to manage. The council is currently spending £55,000 a week on Discretionary Housing Payments to help claimants meet their rent and thousands more on additional welfare and employment support. None of this should be surprising. As a leaked letter from Eric Pickles's office to David Cameron warned in 2011, the cap "does not take account of the additional costs to local authorities (through homelessness and temporary accommodation). In fact we think it is likely that the policy as it stands will generate a net cost. In addition Local Authorities will have to calculate and administer reduced Housing Benefit to keep within the cap and this will mean both demands on resource and difficult handling locally."

At the same time, there is little evidence that the cap is achieving its stated aim of moving claimants into work (principally because few choose to live "a life on benefits"). Just 74 of the 740 Haringey households affected found work, a number no greater than one would expect without the cap given the regular churn of claimants. In many cases, the lack of affordable childcare continues to represent a barrier to employment. Indeed, by requiring councils to relocate families hundreds of miles away, the cap actually reduces work opportunities by forcing them to live in an area where they have no employment history.

The Tories will argue that it is unacceptable for some families to take home more in benefits than others do in wages. But this is an argument for tackling low pay, not for cutting welfare. The claim on which the policy rests - that a non-working family can be better off than a working one - is a myth since it takes no account of the benefits that an in-work family can claim. For instance, a couple with four children earning £26,000 after tax and with rent and council tax liabilities of £400 a week is entitled to around £15,000 a year in housing benefit and council tax support, £3,146 in child benefit and more than £4,000 in tax credits.

Were the cap based on the average income (as opposed to average earnings) of a working family, it would be set at a significantly higher level of £31,500. The suggestion that the welfare system "rewards" worklessness isn’t true; families are already better off in employment.

But to judge the cap on these terms is to misunderstand the government's motives. The cap is less a serious act of policy than a political weapon designed to trap Labour ("the welfare party") on the wrong side of the argument and to perpetuate the belief that the unemployed are to blame for their own misfortune. On this basis, it is working just as intended.