★★★★

In her youth in the 1960s, Charlotte Rampling exuded sexual confidence – feline and slightly dangerous. Tom Courtenay, in contrast, was forever Billy Liar, the stringy, scruffy working-class lad whose life was dwarfed by his dreams.

Both ghosts hover over Andrew Haigh's 45 Years, in which Rampling and Courtenay co-star as a couple whose seemingly tranquil 45-year-old marriage is abruptly threatened by a spectre from the '60s.

In a plot twist freakishly at odds with the quiet island of introspection where the rest of the film dwells, Courtenay's Geoff Mercer receives a letter about Katya, the woman he had loved before he met his wife, Kate (Rampling).

Katya was killed, falling into a crevasse while she and Geoff were hiking in the Swiss Alps. Now the glacier has melted – global warming strikes again – and her body has been found, preserved by the ice. With the Mercers' 45th anniversary party just days away, the weight of memory descends, sending Geoff into a funk.

For Kate, who knew nothing of the affair, it's akin to the discovery of a secret room in a house where you've lived for most of your life. Indeed, the Mercers' attic becomes that room. It's here that she finds diaries and photos which reveal exactly what her husband has neglected to tell her.

Except for the velvety voice and the concentrated gaze, there's little in Rampling's dressed-down, sensible looks to remind you of the siren she used to be.

Kate is a retired schoolteacher and she and Geoff have an old farmhouse in flat Norfolk Broads country with a spruced-up market town nearby and a network of old friends. They present an exemplary portrait in elderly, middle-class stability yet there are indelible traces of the people they used to be. It's in the montage of '60s pop that Kate listens to while choosing music for the party and it's in the glimpses we get of Geoff, the vociferous leftie, known for abusing his friends at dinner parties for their reactionary wrong-headedness.

He still seethes – over the former comrade who has settled into retirement and regular golf games with his banker son-in-law – but these days, the seething is does in private, with Kate as his indulgent audience.

Haigh first made his mark in 2011 with Weekend, about the birth of a gay love affair in the course of a single weekend.

He's an expert in interiors and he's found two able and perceptive collaborators in his leads. The proof is in the delicate play of feeling enlivening Rampling's close-up as she stands staring through a window. And it's in the rigid set of Geoff's shoulders as he sits alone on a park bench, silently viewing scenes from the past – although Courtenay occasionally overdoes the fey and boyish air of distractedness that Geoff has carried into old age.

The camera catches all the intimacies of a long-distance marriage which has reached the stage when sexual desire and physical performance don't match up any more and passion has been transformed into a fond and shared self-deprecation.

The Mercers had persuaded themselves that they'd become resigned to these signs of irrevocable change, but the discovery in the ice has shown otherwise. As Geoff sees her, Katya is his own Sleeping Beauty, destined to remain ageless and live on as a silent rebuke to his own inevitable decline into decrepitude.

In mourning her, he's not only toying with tantalising possibilities forever unrealised, he's grieving for his youth.

For Kate, it's even worse. You can't fight a ghost, so there's no one to blame for the irrational fits of jealousy undermining the state of wisdom she thought she had achieved. As well as frustrated, she feels diminished.

We hope that age puts us beyond desire for the things we can no longer have – that we can grow to accept the evidence of the mirror, difficult as it is. This story, which grows richer the more you think about it, is a rueful acknowledgment of the fact that few of us can.

The heart, no matter what shape it's in, may still beat to the rock 'n roll rhythms reverberating from the soundtrack of the Mercers' anniversary party, which forms the film's poignant and problematic climax.