The day Claire Kober quit as head of Haringey council in north London, I remembered a car ride from long ago. It was 2016, just after Christmas, and I was in a Fiesta, being driven around by a couple from Tottenham. We shared sepia-tinted memories – their favourite park, the market where my mum used to shop – and then they pointed out the vast swaths that Kober’s team wanted to knock down. The estates where thousands of families lived, small businesses trading for generations, the library … all were going to be thrown into a £2bn private fund, the Haringey Development Vehicle (HDV), which would be owned jointly with the developer Lendlease. Then they would be flattened.

That couple had no big organisation, no grand plan – just a determination to stop the bulldozing of their neighbourhood. They had nothing in common with the so-called militants described this week on the BBC and in the papers as having toppled Kober. Momentum? Not members. Bullying? These retirees believed they were going to lose. But then no one I have met in the year I’ve been writing here about Haringey fits the nonsense that’s been spewed about them in the past few weeks.

Some have been eccentric, such as the chain smoker who considered the last minutes before I flew off on honeymoon to be the perfect time to discuss the minutiae of local Labour meetings. Others have been frightened, like the woman nearing retirement who’d just heard that her flat would be among the first earmarked for demolition. But what drives all the anti-HDV protesters is a commitment to their home. As one put it to me: “Kober’s lot see Tottenham as a giant brownfield site, but it’s our lives.”

It would be easy to treat the exit of one of Labour’s most powerful women as being about party infighting. Certainly, Kober’s sexism and bullying allegations should be investigated. But, please, ditch the cliches about Corbynistas and suburban revolutionaries. The death of the HDV is a victory for local people over multinational business, for democracy over machine politics. Most of all, it is an inflection point in one of the great battles of our times: Big Finance versus the rest of us.

The HDV’s defenders claim it was the only practical way of dealing with London’s housing crisis in a decade of brutal cuts. Yet it would have done nothing for the 10,000 households on the waiting list for a Haringey council home. The policy set no explicit target for social housing. I have approached the council press office several times, I have asked a senior councillor on television and another on social media. The response is usually a wriggle of discomfort and then a promise that 40% of new homes built would be “affordable” – a term that in London means its opposite, given the sky-high market rates.

Support for the HDV was the political kiss of death, but the outgoing leadership said it would push through its plans

The Tory press and the Labour right, however, are already painting Kober as a martyr to the Trotskyites – a band that apparently includes David Lammy MP and the local Lib Dems. They claim her exit is an affront to democracy, when Kober and her enforcers ignored two council scrutiny reports calling for an immediate halt; arranged secret meetings with Lendlease, and disciplined Labour councillors who challenged them in public. Checks and balances are always important – but especially in Haringey where, after the horrific death of eight-year-old Victoria Climbié, a public inquiry berated councillors and officials for not asking questions. The inquiry’s chairman, Lord Laming, declared that they “must not accept at face value what they are told”.

Then came the local selections for the May council ballots. Support for the HDV was the political kiss of death for any contender. Though this meant the Labour stronghold council would change entirely within months, the outgoing leadership boldly announced it was going to push through its plans.

Given Kober’s inability to compromise, there is something fitting about the manner of her departure. According to correspondence I have seen, she was invited to Labour HQ for this Tuesday at 1pm to talk to a couple of the anti-HDV councillors – a meeting that would have been chaired by the shadow secretary for local government, Andrew Gwynne. A necessary discussion, to clear up a local mess that was now a national debacle. The meeting never took place. Instead, that morning, she announced she was stepping down.

In many respects the HDV resembles the other big story of this week, Capita. The outsourcing multinational, now in deep financial trouble, has embedded itself in the British state: it runs GP services, hospital parking, the government’s food research agency. In the London borough of Barnet, which neighbours Haringey, the council has outsourced the vast bulk of its services to Capita. Ring your local library and the call is first directed to a Capita centre in Coventry. If you’re a council employee with a payroll query, that’s handled by Capita in Belfast. Residents have labelled Barnet “Capita-ville”. Until this week, Haringey was on the verge of giving the giant multinational Lendlease joint control over local housing, planning and regeneration strategies.

In both Barnet and Haringey, the councils used the financial crisis and the austerity that followed to justify their decision to outsource vital parts of our democracy. But in Barnet, the great outsourcing drive began before David Cameron even entered No 10. In Haringey, the HDV was never just about social housing – it was going to swallow up council offices and park buildings. This was a scheme that in effect would have handed a borough on a plate to Big Finance, in the form of a giant developer. And now it has been beaten, by a band of retired vicars, chain-smoking obsessives and Fiesta drivers.

• Aditya Chakrabortty is a Guardian columnist