Ashley Zhangazha and Don Warrington in Death of a Salesman at the Royal Exchange. Photo: Johan Persson

Memory is so often tied up with place. Certain spaces, certain landscapes, tug us back to moments in our past. Throughout Sarah Frankcom’s new production of Death of a Salesman, a huge canopy of leaves hangs overhead, rustling with recollections of a time when trees filled the neighbourhood. Leslie Travers’ design suggests both the dreamlike realm of memory and the characters’ longing for natural spaces – for a landscape in which they might make something solid and real, rather than chasing the intangible goal of capitalist success.

But while the leaves may flutter above, the ground of reality is dirty and corroded. The circular stage of the Royal Exchange has been made to look rusted and stained – past its best, like protagonist Willy Loman, the salesman approaching the end of his life. This space encapsulates both the dissatisfaction and despair of Willy’s present and the dreams of past and future. Those branches and leaves, forever out of reach, are the idyllic neighbourhood of Willy’s reminiscences, as well as the wide open spaces where his son Biff wants to build a ranch. They’re the jungle where mysterious Uncle Ben made his fortune and the countryside where Willy’s devoted but weary wife Linda wants the family to drive for a weekend picnic.

While it might not allow for elaborate scene changes, the in-the-round auditorium of the Royal Exchange is a particularly effective space in which to evoke Willy’s frantic memories and imaginings. The plain circle of the stage feels like a dream space more than it ever suggests any solid location. But there’s also an intimacy to it, with the audience pressing in on all sides, that draws out the family drama of the play. In Death of a Salesman, we are not just watching one man’s tragedy; we are looking at a family trying to negotiate their fraught relationships to one another.

As Willy, Don Warrington is a distant and withdrawn figure, more fully himself in his memories than in the reality of the present day. In the sun-bathed past, he fills out his clothes, his shoulders rising and pulling back; in the present, he scrunches up in his suit jacket, walking around with just a hint of a despairing hunch. The real strength of the family comes from Maureen Beattie’s Linda, whose habit of gentle accommodation clothes a spine of steel. When she stands up for her husband, her rage and love are formidable. Sons Biff (Ashley Zhangazha) and Happy (Buom Tihngang), by contrast, are all self-doubt and hot air, puffed up and deflated by the empty ambitions of their father.

Death of a Salesman is typically thought of as a play about the American Dream – about the sham of a promise that everyone can rise to prosperity and happiness. And it is about that, of course, in a way that is given extra texture by the casting of actors of colour in the roles of Willy and his sons. If we imagine the Loman men as African Americans, their thwarted aspirations take on a different significance, suggesting the racially unequal distribution of social mobility. Not everyone has the same shot at success.

But watching Death of a Salesman at this moment in time, I’m struck by how much it’s also about a particular idea of what it means to be a man, which turns out to be just as hollow. Much in Miller’s play continues to speak to us, but this implicit critique of a toxic, macho culture feels especially resonant in a world in which the President of the United States exemplifies both the fragility and the dangerousness of aggressive masculinity.

Willy, Biff and Happy have all bought into an idea of manhood as a competition, in which appearances are more important than talent or hard work. They boast of their physical strength and are quick to raise their fists, while Linda’s appeals to reason are ignored. Even at the end of the play, after Willy’s notion of what it is to be a man in modern America has led to his downfall, Happy is poised to repeat his father’s damaging philosophy. The tragic cycle continues; the leaves and the light remain just beyond the characters’ grasp.

Death of a Salesman is on at the Royal Exchange, Manchester until 17 November. More info here.