Throughout the 85-minute running time of Man to Man, I kept struggling to believe that it was Tilda Swinton I was watching on the stage in front of me. Tilda actual Swinton, who many years ago departed the prosaic realm of mere actor to become an icon. Tilda actual Swinton who is, staggeringly, 65, yet to say that she is ageing well is an egregious understatement (does she drink the blood of unicorns for breakfast?). Tilda actual Swinton, who has not been on stage in a play since 1988, when she was once again at the Royal Court performing this exact same role.

The programme is dotted with photos of Swinton’s performance, which I thought were from this current run of Man to Man, Manfred Karge’s German piece for one actor. Swinton being forever young they were, of course, from its 1988 iteration, which came to the Court after making a splash at the Edinburgh Festival.

Since then, Swinton has done many things – slept in a glass case in an art gallery for a week as a piece of performance art; founded a travelling film festival in the Scottish Highlands; won a Best Supporting Actress Oscar for Michael Clayton (2007) – but she has never appeared in a play again, until now. She’s a magnetic stage presence, riveting throughout, and Man to Man makes us dwell wistfully upon what might have happened had Swinton not been, right from the very start of her career, too ethereally cool for school.

Anyone fretting that Swinton has somehow mislaid her cutting edge by performing in something as mundane as a play in a conventional theatre can rest easy: this is anything but a quotidian evening. Karge’s work offers us the character of a German Everyman, who survives against the odds through the turbulent decades of that country’s 20^th century history. Yet, here’s the twist: the Everyman is in fact a woman, who assumes her spouse’s identity and job as a crane operator when he dies at the age of 21.

“I, my own widow,” says Ella/Max and thus we have a shockheaded Swinton with breasts bound, wearing a string vest, men’s red underpants and work boots. You didn’t really think you’d find her in anything as workaday as the frills and ruffles of a costume drama, did you? This is, after all, the woman who made such memorable work of Virginia Woolf’s gender-shifting Orlando in Sally Potter’s 1992 film (I was an impressionable sixth former at this time and it was an unforgettable introduction to both Woolf and Swinton).

It’s astounding to think that when Stephen Unwin’s production was originally staged, even though Swinton looked exactly the same as she does now, the Berlin Wall hadn’t fallen. Karge has added a couple of scenes to cover this, including one with chilling intimations of the rise of the AfD, neatly illustrating once again the inescapably circular nature of history.

Swinton is transfixingly watchable as she stomps about the stage, swilling beer from a can (when she opens the fridge for the first time, the initial strains of Beethoven’s Fifth blare forth from within) and constantly ducking and diving to make ends meet.

Watching her, it is hard not to compile a mental list of all the stage roles at which she would have excelled, had she pointed her career in a theatrical direction: Viola in Twelfth Night (more gender shifting), Lady Macbeth, every female lead in Chekhov, to name but a handful.

However, all is by no means lost and I have a future theatrical suggestion for her. If she prefers not to share the stage with anyone else, how about considering the part of Winnie in Samuel Beckett’s masterful monologue Happy Days? This cheerful and loquacious woman is buried up to her waist in the first act and up to her neck in the second, presenting a set-up that would surely appeal even to Swinton’s indefatigably experimental tastes.

‘Man to Man’ is at the Royal Court Theatre to 24 October