From the knuckles upwards, at least three of his fingers were missing. Frostbite last winter, he said. Some of his toes had gone too. Someone had found him unconscious with hypothermia, and he had spent months in hospital before once again living on the street. He said he needed £17 for a one-night stay in a hostel: I gave him a fiver and some cigarettes, and we talked some more.

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I was in Manchester, covering the Conservative party conference. With work over for the day, I had gone for dinner in the city’s so-called Northern Quarter, where people eat and drink in self-consciously fashionable bars and restaurants, and a steady stream of homeless people tend to circulate, asking for help.

The man sitting next to me at an outdoor table was a case in point. Until a few years ago, he said, he had lived with his mother in Wythenshawe, on the southern edge of the city. When she had died, their social-housing tenancy had ended, and when he had lost his last job everything had fallen to pieces.

When I got home, I was reminded that the viscerally human story he had told me was in line with research and statistics: 83% of single homeless people are reckoned to be men. The average age of death among homeless people is estimated to be 47, around 30 years below the figure for the population as a whole.

The scourge of homelessness and rough sleeping has been growing at speed. A snapshot count by the National Audit Office in autumn 2016 suggested that just over 4,100 people in England were sleeping rough, a figure that had increased by a massive 134% since 2010. At the same point, the number of households in temporary accommodation was reckoned to be 77,000, up 60% in six years.

Facebook Twitter Pinterest ‘Manchester mayor Andy Burnham says universal credit threatens to double his region’s number of rough sleepers.’ Photograph: Peter Byrne/PA

Some of these figures look like underestimates. In Greater Manchester, homelessness is said to have quadrupled since 2010. Homelessness charity Crisis estimates that in 2016 rough sleeping in the UK averaged around 9,000. What really matters, though, is that all of these problems are set to get much worse. A recent study by academics at Heriot-Watt University in Scotland said that if government policy remains as it is now, the number of homeless people in Britain will reach 575,000 by 2041, up from 236,000 in 2016. Over the same period, the number of people sleeping rough could top 40,000.

Little more than a year ago, the official approach to homelessness was still often stuck in a rut of punitive measures and apparent inhumanity: councils imposing fines for begging and rough sleeping, and endless talk of crackdowns and zero tolerance. Now, though, accompanied by a clear sense of political panic, there are the first signs of a thaw, not least at the top.

Yesterday, Theresa May returned to Manchester to seemingly exorcise the ghost of that awful conference speech, and announce a £3.8m contribution to something called the “Greater Manchester Homelessness Prevention Trailblazer” – a means of showing her approval for a new array of measures aimed at getting longlasting help to the region’s homeless people, many of them authored by Greater Manchester’s new Labour mayor, Andy Burnham.

Meanwhile, parliament has recently passed the Homelessness Reduction Act, which will supposedly ensure that councils have increased obligations to homeless people, not least when it comes to the single-person households who currently tend to fall through the net, or what remains of it.

Clearly, all this is proof that homelessness is newly intruding on politics, but it jars against two unavoidable questions. First, as evidenced by its meagre new pledges on social housing, why does the government still seem largely focused on symptoms, rather than causes? And when it comes to the latter, who is ultimately to blame?

The answer is terribly simple, embodied in the fact that all those homelessness statistics show a surge that began in 2010. The Conservative party has long had a streak of cold cruelty, and the obscenities of current homelessness are the result.

Where to even start? Of course, if you cut and cap benefits, leave a snowballing housing crisis untouched and fail to question the specious morals of the market, it will have human costs. When, as chancellor, George Osborne started slashing housing subsidies, hacking down housing benefit and restricting single people under 35 to the meanest of entitlements, where did he think it would all end up?

The answer is stark: Shelter reckons that 78% of the rise in homelessness over the last six years was due to people being evicted from privately rented homes, but that did not give anyone in power pause for thought.

Since 2016, rates of housing benefit paid to people in the private sector – set according to what’s called the local housing allowance, which the Tory/Lib Dem coalition pegged to the lowest third of local market rents, rather than the previous lowest half – have been frozen, while rents have carried on rising, not least in cities.

Worse still, from March 2019 the same limits will apply to housing benefit going to people living in social housing, which professionals say will have a dire impact on one group in particular: again, single people under 35. If they are lucky enough to live alone in, say, a one-bedroom flat in a tower block, they will suddenly have to find accommodation in the kind of shared houses that are lamentably thin on the ground. Not for the first time, you’d think you were looking at a policy designed specifically to increase homelessness.

The impact of benefit sanctions barely needs mentioning. And now comes universal credit, already rolled out in areas scattered across the country, and now set to be extended even further before its full introduction in 2022.

Private landlords are already refusing to let properties to people in receipt of the new benefit, for fear of their tenants going into arrears. Councils and housing associations say that the mandatory six-week gap between making a claim and receiving a first payment is leading to huge problems, and evictions directly related to the new system are already under way.

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Cuts to the so-called working allowance will leave many people thousands of pounds a year worse off. There is palpable anxiety about the most awful of outcomes: life in emergency accommodation, or, if lives truly fall apart, on the street.

In Manchester, Burnham says universal credit threatens to double his region’s number of rough sleepers. “If the rollout goes ahead as planned it will make our problem dramatically worse,” he says.

The words have an air of unintentional understatement, but they highlight two of 2017’s biggest stories: on the streets of our cities, everyday matters of life and death. And in Whitehall, a government seemingly lost in its own cruelties.

• John Harris is a Guardian columnist