The Commons have long departed, the country awaits the joy of archery and weight-lifting, but the House of Lords plods on regardless and disregarded. The few peers who follow the fiendish complexity of local government finance and social security are again toiling over the monstrous deformity that is Eric Pickles' council tax benefit "reform". In myriad ways David Cameron's government is intent on reprising the Thatcher revolution by slashing the state and privatising the public realm. But you might think there was one lesson from her history that he would strenuously avoid repeating – the poll tax. Amazingly, here it comes again.

Day after day the sheer idiocy of this policy and its inevitable implosion into chaos is being exposed to brutal scrutiny in the Lords grand committee. The hapless government minister deputed to respond was last week withdrawn from the committee, mangled by his utter inability to give answers that made any sense at all. The ejected minister was Lord Attlee – who, though he inherited his peerage from the great prime minister, with curious timing joined the Tories on the eve of the 1997 election. He let slip that "the little cut" was to finance new rail investment, which supposedly needs no taxpayer funds. But even his replacement, who was once a council leader herself, is struggling as hard with the committee's probing questions. There are no plausible answers. Everyone knows this is a smouldering conflagration, yet no minister has the wit to call the fire brigade and hose it down.

Here's the background: on average, households pay £1,000 a year in council tax. Until now, households on low incomes were exempt or paid only according to their means, so 5.9m households received council tax benefit. From next April, the benefit is cut by 10%, which is bad enough; but then insanity takes over. Each local authority will be given the sum that was handed out in benefit in their area (less 10%) to disperse as they please. They must keep paying the full benefit to pensioners and "the vulnerable". Each council must choose who is "vulnerable", as the government refuses to provide its own definition. Half of the recipients are pensioners, so protecting them means all other low-income households bear the whole cut, averaging 20%. People who live in areas with a lot of pensioners or a lot of the "vulnerable" will suffer the biggest cuts, as much as 30% or more. The Institute for Fiscal Studies (IFS) says low-income households in Haringey, north London, lose £38 a year.

Benefit expert Lady Hollis points out that if a factory closes and suddenly a lot more people claim council tax benefit, everyone else in the district will have their council tax benefit cut to accommodate the new claimants. It is, in effect, a tontine, a lottery. Since the majority of the non-pensioner poor are in work, this hits the working poor hardest, adding to disincentives to work, when every extra pound they earn can see 95p in benefit lost.

This blows away Iain Duncan Smith's repeated promises that his universal credit, also starting next year, will smooth out all tapers and ensure everyone is always better off working. The government even defended this cut with the assertion that it would incentivise local authorities to find work for their denizens, so as to get them off council tax benefit. Yet the IFS shows the effect to be the opposite: it takes away incentives to work, with too steep a loss of the benefits for those moving into jobs.

By now no one can be surprised by any social injustice from a government that has chosen to see the great burden of its cuts rain down over and again on the same households with fewest resources. But what does amaze is its indifference to omnishambles. Oblivious to all warnings, on it plunges. This "reform" will be a classic case history when the ashes of this government are picked over by the forensic fire investigators.

Follow this: 300 councils must each devise their own criteria. Each becomes a mini DWP, establishing its own means test without having access to people's earnings. Each must divide its benefit pot between varying numbers of claimants each year. Miserly authorities can keep much of it for other purposes. Each decides who is "vulnerable" or whether to include disability living allowance, child benefit or personal savings in declaring who is eligible for how much.

Then councils must collect smallish sums from millions of families who have never paid before, with new billing and recovery processes. The poll tax proved this impossible: debts rose and 5,000 poor people went to prison for non-payment. Since then magistrates and fine collection officers have been cut back. Expect a repeat. Another poll tax effect was large numbers of debtors hiding by taking themselves off the electoral register, a democratic deficit that was never quite repaired.

All this is to save just £500m. Will anyone compute the administrative costs for these 300 local authorities? Many will fail to put this in place in time, so the government will impose its own system on them in January. The usually measured IFS has written a damning report calling the challenge "truly formidable". It warns that councils will have an incentive to move poor people out of their districts and to discourage benefit takeup campaigns. Kindly councils that try to protect their poorer citizens by finding the missing 10% themselves will have to make deeper cuts or raise council tax rates by almost 2%. If they try to protect the very poorest from the cut, that would create such aggressive rates of benefit withdrawal for the other claimants that work incentives are wiped out.

The IFS makes a constructive suggestion: at least let councils, if they choose, abolish or reduce the single person's discount and spend the money filling the gaping hole in so many poorer families' finances. The IFS finds this discount is mainly paid by better-off single people in large houses. But instead of seizing on this small easing of the problem, the government has so loudly rubbished the idea that it can't retreat.

Inefficient, bureaucratic, unjust and unworkable, the wonder is that local authorities are so docile when they should be raising the roof – Labour, Lib Dem and Tory councils alike. This is classic Cameron "localism", devolving the axe and the blame, dumping on councils the responsibilities that belong to central government with no power to raise extra money. The only new local powers are nasty decisions. Meanwhile, the poorest households bear the brunt, yet again.

• This article was amended on 24 July 2012. The original said households in Haringey would lose £38 per week. That has been corrected to £38 per year.