Their faces are hauntingly impossible to ignore, staring out from the front pages. Some are in school uniform, little more than children; others all teenage bravado, hovering on the difficult cusp of adulthood.

But all 27 teenagers were far too young to die like this, stabbed to death on the streets of Britain in the past 12 months. This is the kind of national moment that demands a swift, reassuring and comprehensive response from politicians. And yet what it gets is Theresa May, stiffly insisting that there is “no direct correlation” between the rising tide of knife crime and police numbers. Nothing has changed, or if it has then it definitely wasn’t her fault. It is a characteristically tone-deaf response to a public mood characterised by alarm and sorrow; why can’t she see that dead children requires something more emotionally literate than this? But the bigger problem is that what she’s saying flies in the face of common sense.

It would be disingenuous for police to argue that this was all about money, nothing to do with strategy or even with historic failures to gain the trust of a community. But nobody is saying that funding cuts are the sole cause of a complex social phenomenon such as gang crime (not that all knife crime is to do with gangs, obviously; what seems to have driven the Daily Mail to put those 27 young victims of knife crime on its front page is the fatal stabbing at the weekend of a 17-year-old private schoolboy from Manchester, and police have said there is no evidence that was gang-related). Cressida Dick, the Metropolitan police chief who contradicted the prime minister by arguing that there was in fact a link between police numbers and violence, can hardly be accused of shroud-waving when she also stressed that there have been fewer knife murders on the streets of London this year compared to the same period last year.

The claim is simply that policing budget cuts of £250m since 2010, leading to fewer officers on increasingly dangerous streets, cannot fail to have some impact over time. And the same is true for cuts to every other part of the social fabric: youth services, early intervention with troubled families, mental health, education. These services all existed for a reason and we are once again having to learn the hard way what that reason is.

For May, there is an awkward personal history here. Almost five years ago, at the Police Federation’s national conference, the then home secretary delivered the most crushing of putdowns, a merciless lecture on police failures from the death of Stephen Lawrence to the death of a man caught up in the G20 protests, accompanied by a thinly veiled suggestion that since she had managed to cut their budgets without prompting a rise in crime perhaps they could stop complaining about it. She was heard in largely sullen silence, because if what she had to say was unwelcome, it was also true. There had been failures, and during the Cameron years, austerity did not have the predicted effect of driving crime up. That puzzled some criminologists at the time, but it seems the reaction may simply have been delayed.

This is how Conservative governments almost always fail in the end. They cut and cut, and for a surprisingly long time most people don’t feel the impact; frontline staff work overtime or come up with imaginative ways around the problem, or sometimes it turns out there is more fat to trim than anyone in the public sector wanted to admit. But eventually the nation starts to feel it – first the poorest, then the comfortable middle classes – and that is roughly where we are now. Knife crime is spreading out from London into other major cities, and even sleepy market towns are now experiencing an unexpected surge in violence as the county lines drugs trade reaches aggressively out into the shires. Law and order is being tested to the point where even readers of the Daily Mail and Telegraph are starting to notice, and the country deserves more than a hastily convened knife crime summit in response. Lives, as we are being reminded on an almost daily basis, depend on it.

• Gaby Hinsliff is a Guardian columnist