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POP mythology meets political allegory in “Children of Men,” one of the most vivid and plausible dystopian films ever made and among the most agonizingly beautiful. Agonizing because this is a film about the end of our world, a world that the film’s director, Alfonso Cuarón, insists — despite everything, despite the hate and hopelessness, the brandished guns and spewing smokestacks — is overwhelmingly beautiful. A world that is, as Mr. Cuarón’s visual style argues in image after lapidary image, worth saving.

Loosely adapted from P. D. James’s novel “The Children of Men,” the film was written by Mr. Cuarón along with Timothy J. Sexton, David Arata, Mark Fergus and Hawk Ostby. As the dying human world ignites in the face of universal infertility, Britain carries on under military lock and key. Ms. James’s version of the story involves a lot of fussing about God and cataloging of human error; Mr. Cuarón shows, rather than lectures, and invests the story with the urgency of the present, including military buses labeled “Homeland Security.” Ms. James’s nativity story is, in Mr. Cuarón’s version, set against the image of a prisoner in an orange smock with a black bag on his head, arms stretched out as if on a cross.

The story hinges on an enervated employee of the Ministry of Energy, Theo (Clive Owen), who becomes the unlikely protector of a pregnant woman, the first in 18 years. Theo is no ordinary film hero and Mr. Cuarón, working with the virtuosic director of photography Emmanuel Lubezki, tends to keep his distance from the character. Much of the fluid, graceful camerawork is hand-held (by the camera operator George Richmond), sometimes noticeably so, which makes you aware that another human being is framing these images. That’s especially true when the camera moves away from Theo to show us something he seems to have missed, like cages crammed with weeping, pleading immigrants destined for deportation.

An early encounter between Theo and his powerful cousin Nigel (Danny Huston) lays out the film’s moral and political topography as clearly as would a cartographer. Theo, having agreed to shepherd the woman for money but not yet aware that she is pregnant, hits his cousin up for transport papers with offhand subterfuge. (He might easily be dealing weed.) Nigel hoards masterpieces and knows something about smuggling goods. He is also a smooth operator and sends a Rolls-Royce to fetch Theo, who on his way to his cousin gazes with equal indifference at the penitents massed in Trafalgar Square and the royal guards parading behind the locked gates of St. James’s Park, where the wealthy walk the family zebra.

Nigel works in the Ministry of Art, a foreboding composite structure that borrows its exterior from the Battersea Power Station on the banks of the Thames across from Chelsea and Westminster. Fans of progressive rock know Battersea from the cover of Pink Floyd’s 1977 concept album “Animals,” the one with the floating pink pig and a playlist that includes songs like “Pigs” and “Sheep.” The album seems to have been inspired by George Orwell’s 1945 allegorical novel, “Animal Farm” (the book’s money quote: “But some animals are more equal than others”). “Children of Men” seems similarly inspired by Orwell’s novel (meaning loosely), in that it also concerns totalitarianism, reactionary violence, propaganda and the metaphoric use of animals. The film is also, to borrow the novel’s original subtitle, “a fairy story.”

The scene in which Theo asks for the transport papers opens with him walking into a vaulted room dominated by Michelangelo’s “David.” There is a metal pin where a section of the statue’s left calf once was, and two Irish wolfhounds flopped near the base. When Theo approaches the statue, the dogs stand and growl, creating an overture of sorts for Nigel, who breezes in and strikes a rakish pose that visually echoes those of the statue and dogs. The men chat briefly, then join a third, younger man at a large dining table in front of Picasso’s “Guernica.” This furious protest — which commemorates the 1937 decimation of Guernica by Nazis, Italian Fascists and Spanish Nationalists — has been reduced to wallpaper.

“We got to keep ‘Las Meninas,’ ” says Nigel, “and a few other Velázquez. But we only got a hold of two Goyas. That thing in Madrid was a real blow to art.” Theo replies: “Not to mention people.”

Seated with his back to Picasso’s writhing black-and-white figures, Theo spins a tall tale in a ploy to secure the transport papers. As Handel swells on the soundtrack, Theo continues spinning his lie and a servant tries to serve him: he waves the man away with a practiced hand. Nigel listens to Theo with vague detachment and murmurs a few words about the difficulty of the request (“That’s quite a favor”). He then turns to the third man, who is busily playing some kind of game wired to one hand, and says, “Alex, take your pills.” Alex, his emptied-out eyes fixed on the game, doesn’t seem to hear. Nigel repeats Alex’s name quietly twice more, then roars it. Alex takes his pills without pause, his fingers mechanically tapping.

Nigel beckons Theo away from the table and the two men face each other before a wall of windows. Outside, the pink pig floats in the gray air, defying the burden of its symbolism. Nigel offers Theo a pillbox, and the offer feels like a threat (“Take your pills, Theo,” you can almost hear him murmur). Theo declines with a wry smile. “What?” asks Nigel. “You kill me,” says Theo, “a hundred years from now,” there won’t be one sad soul “to look in at any of this.” Theo turns to take in the room, as if sweeping everything — the wounded statue, the neutered painting, the silent servants, the growling dogs, the pig above, the sheep below — into a careless heap. “What,” asks Theo, “keeps you going?”

Nigel pauses, before stating the obvious. “You know what it is, Theo. I just don’t think about it.”