Three months ago, the education minister Lord Agnew offered to bet any headteacher “a bottle of champagne and a letter of commendation” that he could find wasteful spending in their school. It was a crass, tin-eared remark to make at a time when some schools are closing early on a Friday to save money.

The government’s response to concerns about declining school funding has been tone deaf from the start. Analysis by the Institute for Fiscal Studies shows that real per-pupil funding in England has fallen by 8% over the past decade, the biggest cut to school funding for three decades. Yet the government claims that it is putting more money than ever into schools. But its figure fails to take into account inflation and a significant rise in the number of pupils over the decade. It has rightly been scolded by the UK Statistics Authority for using misrepresented and exaggerated figures. As David Spiegelhalter, the president of the Royal Statistical Society, last year concluded: “For a department that is in charge of the nation’s numerical skills, this is getting embarrassing.”

Schools are having to find savings in ways that cannot fail to have an effect on their pupils’ education. In Birmingham, many primary schools are finishing at lunchtime on a Friday. In other areas, some schools delayed turning on the heating until November. Others have set up Amazon wishlists to encourage parents to buy basic supplies like pens and gluesticks. Some heads report that they undertake tasks such as driving the minibus and cleaning to cope with staff shortages. Little wonder that the chancellor Philip Hammond’s promise of a one-off £400m for “little extras” like whiteboards provoked so much anger.

But schools are coping with more than significant cuts to their own budgets. Schools are truly the frontline public service, the one part of the state that children come into contact with day in, day out. When other services are stretched, they have to pick up the slack.

And what the government has piled at their gates goes far beyond declining school funding. Schools are also contending with even more significant cuts to the children’s services, run by local councils, that support their most vulnerable pupils. English councils have seen their government grants slashed by almost half since 2010. Spending on children’s services has dropped by almost a third across the board since 2010. But it is the least affluent areas with the highest level of need – where councils cannot rely on the council tax base of more affluent areas – that have had to bear the brunt.

Spending on children’s services in the poorest areas has fallen six times as fast as in the most affluent. That means teachers who can no longer rely on social services, on educational psychologists, and on mental health services to support the learning of children with emotional and behavioural difficulties. It’s becoming ever harder for the system to keep children safe, and the rising incidence of knife crime is only one symptom of that.

Not only that, child poverty is forecast to hit record levels by 2022 as a result of cuts to benefits and tax credits for low-income families. Schools are confronting the grim everyday consequences of this, not ministers in Whitehall. Headteachers report children turning up to school grey with hunger; some schools are washing dirty uniforms for families who can’t afford to do so themselves.

Since 2010, Tory chancellors have maintained that austerity is a necessary price we have to pay to get the nation’s books in order. That’s simply untrue: even as they’ve cut services and support for low-income families with children, they have delivered costly tax breaks for more affluent families and businesses.

Set this against Agnew’s champagne wager, or Hammond’s “little extras”, and it’s clear the government has its fingers in its ears on school funding. But it ignores the teachers sounding the alarm bell at its peril. They’re telling ministers something they should have always known would be the case: 10 years of austerity will blight the lives of a generation of children for years to come.