There’s a homeless shelter near my house, which is one of a few reasons why I’ve never seriously considered the possibility that anyone might freeze to death on the streets overnight. The news is full of previously unfamiliar phrases about emergency cold weather provision for rough sleepers “kicking in” when the temperature hits zero. When it gets cold enough, no one is turned away. Shelters start to open during the day. Local politicians, mayors especially, talk determinedly about how to combat homelessness, and charities are mollified and surprised. Yet deaths on the streets have been happening quite regularly since the start of winter. Walking past a guy I see every day, in progressively worse shape, the question mark over whether or not he’ll survive the month arrives not as a thought, more as a disembodied echo. Is it blase not to worry? Or melodramatic to mention it?

The sense that a Conservative government might be callous is not an unfamiliar one: the contention that actual deaths have resulted from discernible policies is one that only slick-looking men on magazine-format current affairs programmes put any gusto into denying. Yet there is a creeping suspicion that the government has completely ground to a halt. Crises don’t erupt, because there is nobody to deal with them. New policies can’t be announced, because there is nobody to make them. The regular business of the state, to maintain its institutions, react to challenge, find solutions, learn from mistakes and – at its very simplest – make sure its citizens survive, has been suspended. Brexit has been consuming all its oxygen since the referendum was announced. It is astonishing that such an amorphous, deadlocked project could have so much impact: but it has suffocated the government’s ability to respond to anything else.

The crisis in the prison service is perhaps the starkest example. No modern state would undertake to lock people up if it couldn’t assure sanitary conditions and basic safety. Yet violence in prisons, both attacks and self-harm, is at its highest levels since records began. Liverpool prison, the inspection of which last year yielded medieval tales of rats and cockroaches, this month saw its third suicide since September. An urgent notification from the prisons inspectorate found that conditions in Nottingham jail had declined to the point where prisoners were in danger of death.

There’s no whisper of a plan, not even a ‘big society' pipe dream of how children will be protected

It can be hard to extrapolate from prisons: it is the most invisible service, which by design has little contact with the wider population. Even a functional state will sometimes fail. Yet this picture of entropy is replicated wherever you look. The chairman of the Local Government Association, Conservative peer Gary Porter, warned at the start of this month that children’s services face a £2bn shortfall by 2020; that “core central government funding will be further reduced by half over the next two years and almost phased out completely by the end of the decade”. These cuts coincide with “an unprecedented surge in demand for children’s services and homelessness support”, with a child referred to council services every 49 seconds.

When a council goes under, a commissioner is appointed, tasked with “assessing the council’s capacity and capability to improve its children’s services in a reasonable timeframe”. He or she has three months to complete it. This is the result of chronic underfunding. It has no democratic legitimacy; there was never an election pledge that children would have their support removed, the better to stand on their own two feet. Worse, there’s no whisper of a plan, no mention of this crisis in the local government finance settlement, no alternative vision, not even a “big society” pipe dream of how children will be protected by someone other than the state.

The social safety net is shot through with avoidable hardship, state-inflicted destitution. Benefits sanctions were found over a year ago to cost more than they save, and yet the regime persists, driving food bank use and homelessness, with financial pressures so intense that they destabilise families and deliver them to the attention of those services that can no longer afford to help. Universal credit has led to soaring rent arrears. Disability assessments are routinely – in two-thirds of cases – ruled unfair by the appeals tribunal. The slash-and-burn gaiety of the coalition government has evolved into something more Kafkaesque: a system that doesn’t work for anybody, on any terms, which is more costly but also more painful, and in which all reasonable objection is met with the blank inaction of a frozen polity.

Meanwhile, the airwaves are filled with constant wild assertions about how the people have spoken and what the people said; that they voted for sovereignty, for the “dream of free trade deals”, for an end to the vile yoke of the single market, for control over borders and therefore destiny.

Even if any one of those desires were as uncomplicated as the rhetoric maintains, nobody, surely, voted for any of those things instead of the regular business of government. Nobody wanted the freedom to hypothetically trade with Australia at the expense of decency in British prisons, or sovereignty in lieu of children’s services. Yet that is, inescapably, the trade-off: perhaps Brexit would have obliterated all other policy whoever was undertaking it, or perhaps its Conservative agents are uniquely bad. I suspect the latter, but the question is another diversion. We talk constantly about the abstract, while the concrete business of government disintegrates.

• Zoe Williams is a Guardian columnist