Reorganisation – or re-disorganisation – is the perennial disease in the NHS. If I listed all the structural acronyms throughout the decades, and the new staff starting new jobs with new brass nameplates, it would fill this page.

This week, Wes Streeting accepted the resignation of NHS England’s chief executive, Amanda Pritchard, after ousting its chair, Richard Meddings, signalling an effective merger in all but name with Streeting’s own department. Whitehall says NHS England will have “a smaller, leaner role”, with thousands of duplicated jobs lost.

Few people will regret the swallowing up of this remnant of the disastrous 2012 Lansley reforms, which fragmented everything in the NHS. Pritchard and Meddings recently suffered an unwarranted pasting by the Commons public accounts and health committees for their lack of “ideas”, but that was hardly fair. They had been barred from revealing the health department’s imminent 10-year plan. And there is a truth that the committees ignored that bears stating here: the NHS is on the turn for the better.

Jim Mackey takes over NHS England, and even those who say Pritchard got the push unfairly tell me they welcome his arrival. Currently CEO of Newcastle hospitals foundation trust, he was head of NHS Improvement with a record of innovation until it was abolished by one of the three Tory health secretaries passing through in 2022. It’s also worth saying that Pritchard suffered six changes of health secretary in three and half years.

I interviewed Mackey two years ago when he had returned to Northumbria healthcare trust, to start a pioneering scheme that others now copy. Failure to bind social care with the NHS leaves more than 13,000 beds in England taken up by old people waiting for a care package.

Mackey set up a care system within his trust to relieve hospital bed shortages. His Northumbria Care is an NHS-owned domiciliary service that bids for social care contracts from local authorities that would usually be awarded to private providers, seamlessly integrating care within the health service. Here is a smooth transition without bottlenecks between the two sectors, with health and social care funded from the same budget, and every incentive to stop patients needing a hospital bed, and to get them home quicker.

He planned to build care homes to take over residential contracts too, if he could raise the capital.

The idea short-circuits the cumbersome introduction of 42 integrated care boards (ICBs). They were designed to bring local services together, but are largely regarded as failing. They lack the clout to knock local heads together so that GP and community services integrate with hospitals. They have no power over integrating local authority social care. Half the ICBs are in debt; they may yet be merged into half that number.

Rarely has top talent moved from hospitals to run ICBs. Instead, many hospitals are forming groups, which may work better than ICBs. These are not big-bang changes and they slide under the radar, but the Mackey model has inspired other trusts to try similar schemes: expect more of that thinking from him.

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The Darzi report laid bare the state of the NHS Labour inherited. Austerity cut everything, including medical training, with huge gaps in staff as the NHS struggled to cope with the effects of deprivation and a far sicker population.

Streeting is rightly wary of boasting about any progress yet, given public outrage over the still appalling waiting lists (7.46 million cases, according to the British Medical Association), as well as ambulance delays, and ailing A&E and GP services. The Treasury, meanwhile, seems happy to say that NHS productivity is lagging and that extra money ploughed in is failing to produce enough improvement. But that’s not the whole story, and the NHS should speak up. The Treasury traditionally sees the NHS as a bottomless pit, but its productivity is being badly misrepresented with faulty Office for National Statistics figures that are eagerly seized on by enemies of the NHS on the right.

Anita Charlesworth, senior economist at the Health Foundation thinktank, says ONS figures only count acute hospital activity, leaving out the 12,000 new virtual hospital-at-home beds. These are costly, but less expensive than actual hospital beds. The stats leave out GP care. Productivity there is rising fast now that GPs are paid to seek advice from specialists, instead of automatically referring patients to them directly: 1.5 million fewer patients have been referred, the department tells me. Instead, they are being cared for in surgeries under guidance. That GP productivity should be counted in.

The department’s own figures show waiting lists falling and the 2m extra appointments promised within a year have been provided months early, with surgical hubs working evenings and weekends, as well as new diagnostic units.

In his last month as chair, Meddings points to widespread improvements, a service “overwhelmed”, but not “broken”, he tells me. GP appointments are rising fast: 98% of surgeries have digital phones ensuring every call is answered, or called back promptly, with half the callers getting same-day appointments, and 70% face-to-face consultations. April’s year end figures will show “NHS productivity up 2.5%, more than any other public service”, Meddings said. He echoed the curious optimism you often hear throughout the NHS, even from those who describe near-impossible tasks undertaken to cope with rising need.

Keep perspective. Trolleys line many A&E corridors, ambulance delays persist, waiting times are horrendous. I hear laments from managers and medics facing the prospect of 4% “efficiency savings” next year, to be achieved on top of already existing deficits, which must also be cleared. (Spoiler alert: they won’t be.)

But there is hope. Times are tough and funding remains below the NHS historic average. But, as the Health Foundation’s Charlesworth says, this is not a repeat of the NHS austerity years.

Statistics are just that, and what they represent cuts through very slowly, so it will take a long time before the public feels and believes in progress. But, for all the turmoil, green shoots are there.

• Polly Toynbee is a Guardian columnist