The prime minister’s Social Justice and Mobility Commission was no feet-to-the-fire unit, hand-picked with the self-flagellation of the strong to ask questions of the government that were as difficult as could be. Rather, it was boiled down to the well-disposed Alan Milburn, the diplomatic David Johnston, the academic Paul Gregg and the Conservative peer Gillian Shephard. It had been slowly eroded, with key posts left empty for the past two years, but the main problem was that it was tasked with an agenda that the government didn’t do anything to further. So all its members, with heavy hearts, have resigned at once. The government, Milburn concluded, “is understandably focused on Brexit and does not seem to have the necessary bandwidth to ensure that the rhetoric of healing social division is matched with the reality”.

It may be the note of sad kindness that makes Milburn’s letter to Theresa May so devastating: he does not doubt her “personal belief in social justice”; he merely sees “little evidence of that being translated into meaningful action”. This puts him at the far-centre of an opposition that typically found May’s equality shtick rather hard to swallow: but of course he is all the more dangerous for that.

If you could use the phrase sting in the tail, of a letter that is stinging from head to toe, the sign off is particularly damaging: Alan Milburn is not stalking off the territory completely. Instead, he’ll be setting up a new social mobility institute, independent of government and political parties, to work with local councils, major employers, and anyone else who may be able to promote equality. There is, obviously, eternal conflict over the role of major employers – the Milburn wing of the Labour party still insists that workers and bosses are on the same side, while the newly ascendant leaders see employers as the source of the low-wage problem rather than suppliers of ready answers.

But that division, fundamental though it is, has nothing on the crisis engulfing the government. The people running the country simply aren’t seen as being competent to effect meaningful change. The social justice commission is unusual only in going public: everyone, from the prison service to the NHS, is looking for a workaround, a way to avert disaster that doesn’t involve Whitehall. With Brexit looming yet shapeless, there simply isn’t the certainty to make even short-term plans for anything else. Currently only scandal can divert attention from the Europe question. When did a major debate last happen whose keywords weren’t “hard” or “soft”?

Now that it’s disintegrated, this commission looks like the noble iteration of a mildly progressive agenda; in fact, it was not that at all. Instead, it represented an attempt by the coalition government to situate the child poverty agenda in a completely new context.

The Child Poverty Act of 2010 had clear targets: a reduction in the number of children living in relative poverty, absolute poverty, combined low income and material deprivation, and persistent poverty. The act came to life with cross-party support, but that was only skin deep. When David Cameron came in with austerity policies that couldn’t possibly deliver on the targets, his party had no problem resiling from them. But the act couldn’t have been abolished, and replaced by the Welfare Reform and Work Act of 2016, without an alternative narrative taking shape. The proposition that all children should be fed, shod and adequately housed, regardless of how hard-working their parents were, is quite a difficult thing to step away from.

So it was merged, as of the Welfare Reform Act of 2012, with the idea of social mobility, as if those two aims were synonymous. Yet they are not: the idea that a smart, disadvantaged kid from Hull ought to be able to become a high court judge is not remotely similar to the idea that the same kid should live in a warm enough house with three meals a day, regardless of how smart he is. To care that the brightest and best should live in a society where their qualities are rewarded is one thing; creating decent conditions for the dimmest and the worst is altogether different.

Logically speaking, the two agendas aren’t antithetical. But politically they are: the mobility agenda ascribes all poverty to the shortcomings of the individual, whereas the anti-poverty agenda sites it as a systemic and structural problem. Arguably, it was New Labour squeamishness around poverty that made this shift possible. Gordon Brown could never quite bring himself to sell his tax credits as necessary redistribution, and instead fell back on a more sentimental fix – it may be an adult’s fault that her wages aren’t high enough, but it can’t possibly be a child’s.

The conversation for the opposition to have now is not how to restore social mobility to its previous, hallowed place in the national discourse, but to build back into the agenda the idea that persistent poverty is itself an insult to society, regardless of the personal qualities of those surviving it. This was the thinking that underpinned the social exclusion agenda of the earliest days of Tony Blair; it is nothing like as alien to the British body politic as the amnesiac Conservatives would have us believe.

Rejoicing in the government’s turmoil is a diversion from an ever-more immediate question: how to prepare for its collapse.