Writer-director Andrew Haigh specializes in small-scaled relationship dramas like his 2011 “Weekend,” about a brief encounter between two gay men. It’s a pattern he follows, though over a longer time span, in this intensely observant portrait of a marriage in crisis after nearly half a century. “45 Years” is an acute but extremely unhurried adaptation of a short story by David Constantine, a lapidary account of what happens to the genteel union of an English couple, Geoff and Kate Mercer (Tom Courtenay and Charlotte Rampling), as a revelation about the distant past gradually shakes the foundations of their present-day relationship.

The news involves the discovery of a corpse perfectly preserved for decades in a glacier—s premise that was exploited to similarly upsetting effect in an episode of the old Alfred Hitchcock Presents series called “The Crystal Trench” back in 1959. In this case the body is that of Katia, Geoff’s first girlfriend, who was killed when she fell into a crevasse while they were hiking in the Alps a half-century earlier. When Geoff, a fragile fellow who’s retired from his management job after suffering a heart attack, receives a letter saying that Katia’s remains have finally been found, he’s shocked. But it’s Kate, a retired teacher whom he’d met only after Katia’s death, who will be even more affected in the aftermath of the news.

That’s because Kate soon begins to realize that Geoff hasn’t been entirely honest with her about how close he was to Katia, to whom he was actually engaged. It turns out that he was contacted because he’s was officially listed as Katia’s next of kin, since they pretended to be married in order to make it easier to get joint accommodations during their trip. And Kate finds him late one night searching about in the attic for mementos of his time together with the dead woman—which will induce her, in turn, to rummage through the old photos herself. Geoff, meanwhile, begins smoking again, and even suggests that despite his weakened state he might travel to Switzerland to see the body. He also grows increasingly withdrawn, reluctant even to attend a long-planned retirement bash with his former colleagues.

Kate tries to keep up the appearance of normalcy—she takes her regular long walks through the Norfolk countryside with the family dog, goes on outings with friends, and attends to all the details of the elaborate anniversary gathering they’ve been planning in light of Geoff’s recent medical problems. The couple shares an impromptu dance at home, and an intimate encounter in bed one night. But all the while Kate’s attitude toward her marriage is changing, her confidence in her husband’s love being eaten away by her jealousy over what he had with Katia and the suspicion that her ghost has been an unseen, unacknowledged presence in their lives for the past forty-five years.

Rampling has a few scenes in which she becomes demonstrative about what Kate is experiencing, but for the most part she paints the changes the character is feeling with subtle looks of desperation, culminating in the subdued anguish she brings to the final sequence of the anniversary party at which she shares a dance with Geoff. Courtenay has the less striking role, but he too shows his skill at quiet understatement. The secondary cast has relatively little to add—this is basically a two-hander—but does what’s required of them. And cinematographer Lol Crawley captures the misty vistas with a degree of nuance that’s a visual mirror of the many facets the stars bring to their performances.

Haigh’s deliberate approach and Jonathan Alberts’ equally unforced editing sometimes give “45 Years” a glacial feel—if you’ll pardon the phrase. But the sensitivity of Rampling and Courtenay fills even the pauses with unspoken meaning.