In 1776, the great prison reformer John Howard visited Birmingham while compiling his landmark report on The State of the Prisons in England and Wales. “The gaol for this large populous town is called the Dungeon,” Howard reported. Inside, the filth, made worse by the faeces of the gaoler’s ducks, was “intolerable”. The prison itself was overcrowded: “At some particular times, here are great numbers confined.” Overall, he concluded: “The whole prison is very offensive.”

Two and a half centuries later, the prison inspectorate’s conclusions about Birmingham prison, 2018 version, are uncannily similar to what Howard found in 1776. “The prison was in an appalling state,” the chief inspector Peter Clarke told the justice secretary at the weekend, directly echoing Howard. Wings were “filthy”. Windows were out. Cockroaches, rats and other vermin were “widespread.” Safety had “completely failed”. Prisoners used violence “with impunity”. Drugs were everywhere. Inmates cowered behind doors through which urine and faeces were squirted. Bullying was at an “appalling” level. Staff locked themselves away. The inspectors’ own cars were torched during their visit. Birmingham, Mr Clarke wrote, was “in a state of crisis that is remarkable even by the low standards we have seen all too frequently in recent years.”

If it is nothing else, Mr Clarke’s report is a vindication of the prisons’ inspectorate’s long established practice of conducting unannounced inspections – a tactic which other inspectorates in other fields should emulate. His conclusion – “no confidence” in the private operator G4S’s ability to turn things around – has implications for other sectors too. The response from the prisons minister Rory Stewart, who visited the prison himself last week, has been decisive. On Monday the Ministry of Justice took over Birmingham for an initial six months. Mr Stewart promised a handpicked new governor, 30 extra officers and a cut of 300 in Birmingham prison numbers. He could not have done less.

The concern, however, is that this is merely sticking plaster to deal with a broken system. It is true that in some ways Birmingham prison is special. Its record has been unusually up and down: handed over to G4S as a failing prison in 2011, an upbeat report from the inspectorate in 2014, a serious riot in 2016, a bad report from Mr Clarke last year – and now the emergency ousting of G4S. But it is also true that the crisis in the English prison system is a combination of failures caused both by privatisation and also by public sector austerity.

G4S’s staffing in Birmingham is widely seen to have been inadequate and relatively inexperienced; staff retention has been poor. And Mr Clarke’s vote of no confidence is a devastating verdict that no minister can ignore. But don’t blame everything about the Birmingham crisis on privatisation alone. Austerity has taken its toll too. The truth is that Birmingham is a particularly troubled prison, for which privatisation has proved inadequate, and which has paid the price for systematic government prison expenditure cuts of up to 40% that have prevented the investment in buildings, staffing and regimes that it particularly – though not uniquely – needs. As the prison governors argued in response to Mr Stewart’s decision on Monday: “this is not about Public vs Private but about ensuring prisons are adequately funded.”

That is the real challenge that faces Mr Stewart, and not just in Birmingham. The prisons minister got a lot of attention when he said last week he would resign if his pilot reforms to combat violence and drugs in 10 prisons had not worked by next summer. It was a bold pledge from an able and interesting minister. Prison reform will certainly not happen unless ministers like him can deflect people who should not be in the system away from prison. Yet Mr Stewart is unlikely to be in office in 12 months’ time unless Philip Hammond is listening. It is the chancellor – not Mr Stewart – who really owns the Birmingham crisis, and Mr Hammond is currently sweating other departments – including justice – for further savings to free promised extra spending for the NHS. The NHS is popular; prisons are not. But government has an undeflectable responsibility to provide both.