RoosevElvis (Royal Court)

Elvis Presley had a Theodore Roosevelt quotation hanging above his desk at Graceland: "It is not the critic who counts…" – that one. "The credit belongs to the man who is actually in the arena." It is a call to arms; a rallying cry to get up and go, to impose oneself on the world.

Ann (Libby King) – Annie to her imaginary friends – is more like the gender-fluid woman in the dead-end job. A meat factory worker with a bit of a gut and a fringe to hide behind, she's listless and lifeless and anxious. The only thing Ann imposes herself on is the sofa. Her fling with the breezy Brenda (Kristin Sieh) peters out because she can't keep up the façade of her online profile over a three-day road-trip to Mount Rushmore.

Each night, Ann gets home, swigs a beer and channels Elvis for company. He's the man she's not, all cocksurety and swagger; the sort who steps out on stage even after a death threat. King wears him well, dropping her voice to his uh-huh-huh bass, cracking her knees and jutting her jaw. Elvis, in turn, summons his hero: Teddy Roosevelt, America's youngest ever President, played by Sieh with an ear-to-ear muttonchop moustache and a nimble, itching-powder restlessness. Together, the three of them – Ann, Elvis and Teddy – take off for Graceland, via the canyons and highways, motels and diners of every American road movie ever. (Andrew Schneider's on-location videos are lush.)

Roosevelvis's meat is in that collision. The juxtaposition of President and popstar encapsulates something vital about masculinity. Both were voracious meat-eaters, kept fighting fit and understood, without doubt, their right to reshape the world. Today, Elvis is splashed across Vegas. Teddy stares out of a mountain.

That they're played by women adds an ironic distance, as they compete, bicker and, at one point, box bison in the Badlands. Rachel Chavkin's production treads a tightrope of ambivalence: advocating that confidence, but also wary of it's impact – on the environment and on the future. RoosevElvis charts a lineage of heroes – Teddy channels John Muir – like a set of inspiring Russian Dolls. Certain men inherit the earth. The meek, like Ann, get nothing. The same patriarchal values trickle down.

Image is key too: the way we present to the world, the identities we construct online, and our failure to measure up to our sense of self or our sense of others. It is, amongst other things, one of the best portraits of depression I've ever seen: as Ann, King's face hangs slack, as if even expressions require too much energy.

There are lulls. Teddy and Elvis have no narrative momentum of their own: their skits add levity, ideas and drag. Their journey, neither escaping anything nor aiming anywhere, is less a road trip than a spirit walk. Ironically, as constructs of Ann's imagination, they can't impose themselves on the world, only on Ann. She's the story's heart and it's her achievement – hauling herself to Graceland through that fug of depression – that redeems any meandering en route.

There she walks along a wall crammed with scratched signatures – Karen Hamleish '98, Yvette Loves Elvis, PETE – runs her hands over it and, sobbing, adds her own. Ann is not alone, either in her love for Elvis or in getting to Graceland, and there's both comfort and horror in that. There are billions of us in this arena, each fighting our own fight, striving to do the deeds.

RoosevElvis runs at the Royal Court until 14th November.