If there is a cinema of the dispossessed, then its hero has to be the Portuguese film-maker Pedro Costa. His static, austere and often dreamlike movies – unfolding in a mysterious, forbidding semi-darkness – are about marginalised souls, often those in the impoverished (and now demolished) Fontaínhas shantytown in Lisbon. His new film once again reminded me of the pure Beckettian bleakness and starkness in his work: its characters are lonely unsmiling people living below the poverty line who have endured much. Their material wretchedness is not endowed with a condescending nobility but with a serenely laconic self-reliance. Costa and cinematographer Leonardo Simões have composed strangely compelling images of crumbling walls and shadowy, tatty interiors, picked out with fierce key lights to give them an almost modernist look, as if they were studio sets. Almost all of the film takes place at night, except the very end, when there is daylight and even sunlight. The result is weirdly moving.

Once again, Costa is using a nonprofessional actor and telling her real story. Vitalina Varela is from the island of Cape Verde, a former Portuguese colony, who appeared briefly in Costa’s 2014 film Horse Money and now takes centre stage. She has a massively imperturbable dignity and limpid gaze. In the mid-1980s, Vitalina was married to a man with whom she was building a family home, brick by brick. (There are some quietly amazing reverie-like flashbacks to their lives together on the island.) But Vitalina’s husband ran out on her and went to Lisbon, having promised her that he would send money, or at any rate bring her over to join him.

But he never did. Now, after 40 years, Vitalina has finally come to Lisbon to confront him. (There is an extraordinarily surreal, if atypically showy, scene in which the plane is on the tarmac – at night, of course – and Vitalina’s silhouette is dramatically revealed in the open door as she waits for the steps to be brought over.) She discovers, though, that her husband died just a week before. There is nothing left for Vitalina to do but visit the ghetto flat where he lived. She now haunts it like a ghost, brooding over photos of his other woman and occasionally exchanging sparse words with his neighbours.

Then Vitalina recognises someone from home. The priest who conducted her late husband’s funeral ceremony (the one she just missed) is a man she knows was once driven half out of his mind by shame and grief: back in Cape Verde, he refused to baptise a coach-party of people who had arrived without having completed the proper paperwork. He sent them away, and their coach crashed horribly, condemning them to agonising deaths – and the priest to an irrational sense that he or God had done something unforgivable. Now he, too, is a refugee in the uncaring imperial mother country of Portugal: ageing, ill, with a tremor in his right hand. He is played by Costa’s veteran repertory actor Ventura.

Facebook Twitter Pinterest Opaque grief … Vitalina Varela.

Vitalina and the priest should have much in common, but she is exasperated by his assumption that her husband was a victim to be respected and pitied, a poor man who died a lonely death. “Men favour men!” snaps Vitalina. “When you see a woman’s face in the coffin, you can’t imagine her suffering.” And for two hours, we have the challenge of imagining Vitalina’s own suffering, her need to surmount that suffering, her implacable will to survive and her silent, defiant resilience after being cheated of a confrontational moment that would have brought closure. The fact that we know all this actually happened to the woman on screen is both a revelation and a concealment. Like many nonprofessional actors in movies, Vitalina is directed so as to present a calm, unexpressive face to the camera. Perhaps that style is withholding what she feels, and creating a fictional persona of opaque grief.

This film demands a great deal of attention, but to me it works better than Costa’s widely admired Horse Money. There is an immersive deep-seriousness in Costa’s otherworldly artistry – and moments of pathos, such as when Vitalina starts reading aloud from a scrappy newspaper clipping about, of all things, Princess Elizabeth’s first meeting with Prince Philip in 1939. Does Vitalina wonder about the destiny of her own life, betrayed by a man who eluded her, even to the last? She is like a monument to her own stoicism, and her transcendent indifference to our pity radiates from the screen.

• Vitalina Varela is released in the UK on 6 March.