In the beginning, there is only the voice. Unseen, a woman is speaking into a telephone. We hear, but do not see, her grow increasingly exasperated at the crossed lines - she is not Dr Schmit! - as she struggles to connect with the lover who is leaving her to marry someone else.

It is a brilliant opening from director Ivo van Hove, who has here dispensed with almost every stage direction set down in Jean Cocteau's La Voix Humaine (The Human Voice): there is no woman stretched across the floor 'in what could be the scene of a murder'; the suggested clutter of her bedroom has been cleared away. There is only the woman entering a brightly lit box, and, with more than a nod to Rear Window, us voyeurs peering in from the dark outside.

Van Hove has also shifted the telephone itself from the centre of this 70-minute monologue piece, in which a conversation, both real and imagined, takes place between a woman and her lover as he exits from her life. Obvious anachronisms in this 1930 text are updated or circumvented: the fur-lined gloves, the pink dress with velvet collar are gone; and the woman doesn't address the operator by name. She speaks into the remote handset of a landline, while her mobile lies charging on the floor. It is the twenty-first century, but the man could be calling from somewhere with bad coverage. The language (refracted through Dutch back into English surtitles) feels completely contemporary.

What could perhaps seem out of time is the woman's total dependence on her connection to this man (even if she is the kind of woman who wears a Mickey & Minnie sweatshirt), his call supplying an oxygen line that keeps her alive. This modern woman dropped all her friends, one by one, to devote every minute of five years to a man who could not be hers – hardly sensible behaviour. But played out as it is, in a room on what could be the twenty-fifth storey of a high-rise looking out over endless high-rises (including the one we, the voyeurs, must be in), it's an isolating world where the loneliness and desperate actions of an individual make sense.

Contained within the pale walls of what could also suggest a padded cell, Halina Reijn's extraordinary, layered performance leads us step by step, deeper into her despair – but on no simple downwards trajectory. There are moments of hopeful conciliation, regret, pleading, self-effacement, checks and controls – she tries every way to communicate, just to keep the other voice on the line.

Reijn's performance is completely natural in an unnatural space. We see it in the futile gestures she makes to emphasise what she is saying on the phone; the actions that give the lie to the words she speaks into the receiver; and her inability to find a place for herself and her despair in the blank room. In perhaps her ultimate achievement, there is one actor on stage but Reijn creates two: we almost hear what the man is saying, his tone of voice. (Occasionally we admire him for his patience, for calling back.) It's as if La Voix Humaine was written for her.

And yet, despite this immense performance from Reijn, it is difficult to truly connect. The intensity of her performance is somehow made distant by being played behind glass in a set that otherwise perfectly reflects the woman's total isolation. In the same way that Rear Window is about observing from a distance, guessing but not actually knowing what is going on – here we are hearing the human voice at a remove, save for two moments when the woman hauls open the window and climbs out onto the sill, as traffic passes far below. The result is that we are watching this woman from a detached place, and it is hard to feel moved.

In a production that has made such careful artistic choices, the soundscape seems inelegant in design and execution. (No credit is given for sound, which might be a clue.) We have Beyoncé cheering on all the single ladies, and yes, there is the David Sylvian connection with Jean Cocteau, but Paul Simon's 50 Ways to Leave your Lover as the woman most likely leaps to her death at the end is an inexplicable pun that makes light of everything that has gone before.