It's something of a given that wedding anniversaries are loaded with risk. Anniversaries can be forgotten, undervalued, overplayed; by their very nature, they draw attention to the fact that a couple are still together, a state of affairs that may not survive too much scrutiny.

A couple of years ago, the fabulously bitter comedy Le Weekend charted a couple’s 30th anniversary weekend in Paris, the trip exposing the fault lines in their marriage. As its title suggests, Andrew Haigh’s drama covers an even longer anniversary, but proves again that time alone isn’t a reliable barometer of the strength of a relationship.

Kate and Geoff Mercer (Charlotte Rampling and Tom Courtney) have the trappings of a comfortable life in retirement, in their lovely, relaxed home in the countryside. As they approach their 45th anniversary party, Kate is taking care of the preparations, while an unshaven Geoff remains in his pyjamas at home, yet this discrepancy doesn’t cause friction. They appear to be happy.

But then Geoff receives a letter in the post and surprising news. The body of his lover of 50 years ago, pre-dating Kate, who tragically disappeared down a crevice in the Swiss Alps while they were on holiday, has just been found. By all accounts, she is very well preserved. Geoff is shocked at first, as he would be; Kate, who knew of her predecessor, says supportive things, as she should. But with days to go before the party, "my Katya", as he rather stupidly refers to his tragic ex, has taken over the agenda.

Haigh's first film, Weekend (no relation to the aforementioned comedy), concerned the beginning of a relationship between two young gay men. On the surface 45 Years, with its focus on sixty- and seventysomethings intimate for decades, could not be more different. Yet there are similarities, in particular in Haigh's attention to the way people open up to each other, what they say, what they conceal, to what degree honesty is the best policy. What is different here is the age-old question it raises about long relationships: how well do you really know your partner?

Our perspective throughout is Kate's, as she struggles to suppress her jealousy. "I can hardly be cross with something that happened before we existed," she tells her husband after day one. That's true, but difficult to remember when he keeps banging on about Katya and disappears into the attic in the middle of the night to look over his holiday snaps.

There is little in the way of histrionics here, merely two adults, in that very English way, trying hard to ignore or skirt around their true feelings and maintain the status quo. They almost succeed during a cute and funny evening that reveals their genuine connection, the couple first dancing to old 1960s favourites, then comically attempting sex – the sequence added considerable frisson by the fact that the two stars were amongst the coolest icons of the Swinging Sixties.

Yet more and more cracks appear, including a potential reason for their being childless. And Rampling, those lizard eyes of hers as potent as ever, conveys the torment of a woman contemplating the possibility that her entire marriage has been built on, if not a lie, than a consolation. That's quite a hard feeling to shake off.

Haigh’s device for introducing chaos into this couple’s life may be highly unusual, yet the emotional repercussions it delivers are painfully familiar. And in the hands of two consummate performers, the result makes for quietly, profoundly devastating drama.