What will a Corbyn government actually do? Brexit aside, British politics has no bigger known unknown. The prospect fills the rich with fear and the left with hope. Both sides assume that Prime Minister Jeremy Corbyn will be defined by his radicalism, yet in one corner of Britain an arm of the state is already ruling in his name. And the early results are sobering.

In the north London borough of Haringey, the Blairite council leadership was deposed by Labour members a few months ago and replaced with avowed leftwingers. Said the new council leader, Joe Ejiofor: “Over the next four years, it will be up to us to show everybody what this mythical beast the Corbyn council does.” The title may not have been of his making, but by God was he going to wear it. “It is for the many, not the few.”

Everybody cheering that May morning knew what he meant. No more slinging families out of their homes to clear way for multinational developers. No more machine politics and trampling over communities. No more of the politics of contempt.

It was the willingness of the previous leader, Claire Kober, to hand swaths of the borough over to giant building companies that forced her out of office. The Corbyn councillors know they’ll be judged on how far they protect locals from a predatory property industry, which is why they have cancelled the terrible Haringey Development Vehicle. But a real case study of the possibilities and pitfalls of Corbynism in government can be seen right now, in the battle over a small market in Tottenham.

Everyone’s first impressions of Seven Sisters market are terrible. No signs welcome passersby, and the front is almost truculent in its tattiness. But venture inside, and, as another Guardian contributor wrote of a visit: “Within a minute of arriving it was obvious to me that it is irreplaceable.” Because it is magic: a warren of stalls, customised with wooden balconies and eaves, where nearly all the shopkeepers are from Latin America. They sell Colombian coffee and Argentinian meat and films from back home. The soundtrack is a babble of Spanish and salsa. Latin Americans, among them Corbyn’s wife, Laura Alvarez, flock here from across the capital.

“Without this market, the community would have a mental breakdown,” says Vicky Alvarez, who runs a hairdresser’s. In a city that brags of its openness to the world, here’s a corner that bears that out. In a nation of shopkeepers, here are migrants grafting to realise their dreams. About 80 families rely on the so-called Latin Village for their living. Generations of kids have been raised here, playing in the plywood warren. Alvarez says, “We are like meerkats, watching over each other’s children.”

It may take a village to raise a child, but it has taken migrants to raise this village. I remember when this place was semi-derelict.

Anywhere else, the Latin Village would be a prize attraction – but Haringey has decided it should be knocked down and handed over to Britain’s biggest private residential landlord to redevelop. Grainger’s plans include nearly 200 homes, not one of which will be at council rent. The architects’ drawings show a Costa and a “Pasta Express”. It is BlandTown, and Labour signed off on the lot. The politician who has done most for the largely Corbyn-supporting traders is a Tory: Boris Johnson, as London mayor, decreed that the indoor market had to be protected.

‘Everyone’s first impressions of Seven Sisters market are terrible.’ Photograph: Alamy

Like many of the headaches that await Prime Minister Jez, this was one Ejiofor’s team inherited. The complication is that a key part of the land, which sits right above a tube line, is owned by Sadiq Khan’s Transport for London (TfL). Yet the Corbyn council has made the issue worse. It needed someone in charge of regeneration who was allergic to the charms of property developers, but the new leader has instead appointed Charles Adje. Just a few years ago Adje was suspended as a councillor for covering up an official note warning against giving a licence to an especially controversial developer. Asked about this, the council says Adje “made an error of judgment”.

Within weeks of becoming leader, Ejiofor received a lawyer’s letter from traders in part detailing their problems with the man who owns the lease to the market. Jonathan Owen was last year reprimanded by TfL for phrases such as “bloody illegal immigrants”, and declaring at a meeting that “if I wanted to, I could get rid of 90% of the traders here”. The official investigation I have seen notes that he has apologised for the behaviour. He remains in place, paying £60,000 a year for the lease while taking what stallholders conservatively estimate is £340,000 in rent from all of them. The traders have previously offered £100,000 to manage the lease themselves, but TfL took the lower bid.

Very little of that money seems to have been reinvested in the market: carpet tiles are broken and filthy and the electrics keep breaking, so the cafes and butchers’ foodstuffs rot. Questioned about this and other issues, Owen offered no comment. When traders asked last month whether the drains could be unblocked, Owen’s reply was: “When was the last time you cleared the drains in your house?”

This is the Corbyn council’s first big test, and handling it ought to be simple. They’re supposed to take the side of the people, not builders. Their manifesto promises: “Where we have to regenerate parts of the borough, we will bring residents with us.” At a meeting this summer opened by Corbyn ally Chris Williamson, Labour members across the borough voted to stop any demolition of Latin Village, and to save it as a “cultural asset”. Ejiofor’s team has a mandate; it’s just not upholding it.

Rather than taking up the traders’ case, Ejiofor and Adje have fobbed them off. Instead of Haringey cracking down on the market manager, last month it sent an enforcement officer to hassle traders. A pregnant woman running a nail bar was found without a licence, and told to close the shop. In a complaint that I have seen, she said she had felt “embarrassed and humiliated” in front of customers and neighbours. Days later, she miscarried.

This small story carries big lessons for all those hoping for a radical alternative in national government. Ask Haringey cabinet members why they have handled this so badly, and they complain about having a plateful of poison pills left by the last lot. One says: “It’s so difficult to shift the bureaucracy.” Any Corbyn administration will face both of these problems, multiplied a hundredfold.

None of the above is intended to damn a council leadership that’s only five months old and which has some good ideas about cutting council tax for the working poor. Nor is it meant to put on the frighteners about a Corbyn government. But any new Labour administration will be judged on how much change it makes for the people it claims to represent, and how far it represents the social movements whose energy it draws upon. This is the age-old tension of Labour in government, and it will be felt especially keenly by a social-movement politician like Corbyn.

Locally or nationally, no radical government will have it easy. Money will be tight, and Britain has political and economic structural problems that will take decades to put right. Which is why the case of the Latin Village is so instructive. A council must be able to pick the right side in a fight as small as this. It ought to be able to follow some basic principles. Let traders run their own market, and invest in the Latin Village as a local gem. A bit of imagination, a dollop of willpower, lashings of principle. The Corbyn council should learn from this case. Its supporters expect better; the traders deserve better.

• Aditya Chakrabortty is a Guardian columnist