As self-starved IRA member Bobby Sands in “Hunger,” Fassbender gave a performance so frighteningly physical it seemed almost as committed an act of martyrdom as his character’s. He matches that achievement here and in some ways surpasses it, enacting a more figurative form of imprisonment and self-mortification. Completely unself-conscious about the full-frontal nudity and graphically simulated sex acts required of him, the actor peels back layers of lust and self-loathing to become a consummate vessel for the director’s intentions. Even when he says nothing, which is most of the time, Fassbender transfixes.

Sporting a short, bleached-blond hairdo and often clad in vintage garments that clash with David Robinson’s otherwise gray, toned-down costumes, Mulligan energizes the picture with a spirited, sassy turn that at one point also requires her to bare herself for the camera. Her character’s musical solo midway through the film, filmed almost entirely in a single closeup, is one of many exquisite interludes that give this tough-minded picture a soul. So, too, does Nicole Beharie, wonderfully real and affecting as Brandon’s co-worker Marianne, whose attempts to kindle a flame become the film’s heartbreaking centerpiece.

Different as they are, these siblings clearly share a self-destructive tendency, the sources of which lie somewhere in the background, beyond the reach of the film’s curiosity. “We’re not bad people,” Sissy says in a teary message she leaves on Brandon’s cellphone. “We just come from a bad place,” a place specified only as New Jersey… 

More problematic is his reliance on moments of showy cinematic beauty — a long nighttime tracking shot, a Hudson River sunset seen from a high window in the Standard Hotel — that serve at once to alleviate the film’s harshness and undermine its rigor. And the impulse to explore Brandon’s problem in some kind of narrative leaves “Shame” caught between therapeutic melodrama and melodramatic despair. The climax is, for Brandon, a chaotic downward slide that blends provocation with a scolding, breathless moralism. How far will he go? He’ll have sex with a man! With two women!

Is “Shame” the name of something Brandon does feel, or of something the filmmakers think he should feel? The movie, for all its displays of honesty (which is to say nudity), is also curiously coy. It presents Brandon for our titillation, our disapproval and perhaps our envy, but denies him access to our sympathy. I know, that’s the point, that Mr. McQueen wants to show how the intensity of Brandon’s need shuts him off from real intimacy, but this seems to be a foregone conclusion, the result of an elegant experiment that was rigged from the start.

There is a plot, of sorts, amid the pulsation. Brandon’s sister Sissy (Carey Mulligan), a part-time chanteuse and round-the-clock whirligig of neediness, comes unexpectedly to stay. He finds her naked in the shower, thus grazing another taboo. At one point, in a ritzy bar, she unveils the still heart of the film, her face trapped in closeup while she croons “New York, New York,” at a crawling tempo. Mulligan gives it her all, but, as so often in “Shame,” you can’t help considering the context. Would everyone in a New York hot spot go quiet for five minutes in order to listen politely to what is, in essence, a private distress call? McQueen, aided by his screenwriter, Abi Morgan, has stitched together a bespoke idea of the city rather than the place itself, in the same way that he frames erotic pursuit more as a neat conceptual art work than as the farrago of lunging, dithering, yearning, and near-farce in which most of society wallows. To Brandon’s credit, he tries to proceed normally with Marianne (Nicole Beharie), a colleague from the office, taking her to dinner and making non-horny conversation, but, when they finally arrive at the boudoir, guess what? He can’t get it up. McQueen might as well have hung a sign around Brandon’s neck that read “Warning: Cannot Mix Emotion and Sex.” If you want to see the same bafflement, vented with ten times the subtlety, check out Warren Beatty, in “Bonnie and Clyde,” slumping away from Faye Dunaway and murmuring, “I told you I warn’t no lover boy.”

Yet, for all this, “Shame” compels attention. Amid its pious devotion to the woebegone, there are scenes that manage to twitch into life and hit a nerve, perhaps because they also bump the funny bone. Take the wordless subway ride, early in the movie, that finds Brandon, impeccably swathed in coat and scarf, sitting diagonally opposite a young woman. To witness the back-and-forth of their flirtation is like watching Nadal versus Federer on clay. Topspin smiles are dinked across the car, lips are slyly moistened, and McQueen even lobs in a late twist, as the woman proves to be wearing not just a kindly smile but a wedding ring—a combination guaranteed to stir our hero’s loins. The entire sequence is perfect, and PG-rated, and if “Shame” had stopped there it would have been a poem. Instead, there is a novel’s worth of grinding still to come, and, by the end, all that I could think of, however respectful of the film’s aplomb, was the brisk advice delivered by the aging Flaubert to his satyr of a protégé, Guy de Maupassant, in 1878: “You complain about fucking being ‘monotonous.’ There’s a very simple remedy: stop doing it.”

The Iron Lady is a performance in search of a film. The fact that the performer is the esteemed American diva Meryl Streep, and the subject is the contentious British icon Margaret Thatcher, adds up to a very good reason to see this picture.

Unfortunately, it’s the only reason.

Hitting the accent hard with note-perfect emphasis, wearing the upswept do with metallic panache, and playing Thatcher over a 40-year span from her rise to the throne of power through her descent into the throes of dementia, La Streep puts on another superb acting clinic.

But, thanks to a script muddled in intention and messy in structure, she’s acting in a vacuum that eventually suffocates not only her but us too. In the end, we learn, and feel, nothing.