The spirit of Elia Kazan lives on in this tough community drama from Icelandic film-maker Grímur Hákonarson, who won golden plaudits for his 2015 picture Rams, about two sheep-farming brothers, which struck a clever tonal balance between comedy and tragedy.

The County is dourer than that, though from the same world of self-reliant and pugnacious souls who have made their way in life against tough odds, thriving in solitude and hardship amid a vast, remote, beautiful landscape. The action centres on farmers: Inga (Arndís Hrönn Egilsdóttir) who is married to moody, careworn Reynir (Hinrik Ólafsson).

Their life is hard. They are fighting against mounting debts and must work harder and harder to stay afloat. Hákonarson shrewdly begins with a classic farming scene, which for Britons is like something from James Herriot: a calving that Inga handles herself without any outside help, using chains attached to the hooves, steadily, competently pulling. It’s a scene that crystallises her approach to work: calm, professional and with an uncorroded sense that focused effort will be rewarded.

Reynir’s worldview is bleaker. Like his wife, he has become embittered by his farm’s relationship with the all-powerful local co-operative and its political adjunct, the Agrarian party. They’re signed up to the co-op, like all the farmers thereabouts, and this body gives them a safe captive market for their milk and meat, a discount store and loans. But in return the farmers have to buy everything from the co-op itself, at inflated prices. The co-op has become an exploitative racket, a Carnegie-style company store, led by its sinister, desiccated chairman, Eyjólfur (Sigurður Sigurjónsson), who runs a menacing, Stasi-mafia organisation against any farmer who dares go outside the union – using a key informant who betrays his neighbours.

This is a film about the clash of old and new. Inga takes on the co-op, armed with her personal rage and her conviction that the times are a-changing. Farmers don’t need the co-op, she thinks – and she believes that the big international corporations can help her. She can buy materials from Amazon and sell her milk direct to the public via the internet, and she uses Facebook to publicise her campaign against the co-op’s restraint of trade.

Whatever objections everyone else might have to Facebook, Inga is glad of it. Other farmers are fainthearted about standing up to the co-op, but Facebook’s got her back. The mainstream media also take an interest in this maverick woman, and the menfolk are deeply irritated by her. Her fightback involves a moment weirdly like the climax of Ken Loach’s I, Daniel Blake, and there is less political irony in the comparison than first appears.

There’s something else, too. Egilsdóttir’s excellent performance as Inga shows us that, as the gruelling action continues, she looks younger and younger, just when you might expect her to become grizzled and aged by this nasty battle against a local bigwig. It is as if this struggle has given her a new vitality, which wasn’t provided by back-breaking 24/7 work to pay off a crippling mortgage. Her enemies threaten her with bankruptcy. But this threat, so far from scaring her, does the opposite.

Egilsdóttir portrays a woman who is thrilled, not just by the principled confrontation with these local bullies but the prospect of just being rid of everything. So she goes bust – and loses everything – so what? Watching this film, we can see how her farm and all its cumbersome expensive equipment and outbuildings are just a burden to her, and work itself (that sacred shrine to which she was otherwise loyally ready to sacrifice her entire life) is a meaningless treadmill that she has found a heroic and spectacular way to jettison.

The climactic scene at a town-hall gathering is maybe a little contrived, yet Egilsdóttir carries the drama, and her overwhelming feeling of relief makes sense of that gigantic landscape. At last, it is a world to be free in.

• The County is on Curzon Home Cinema from 22 May.