We're greeted at the door by a woman in camouflage overalls, holding a Geiger counter (oh, all right, a bleeping iPhone) in her hand. It's bad news, I'm afraid: World War III has broken out, and we're the last few survivors to have made it down to this cramped and sealed bunker. But all's not lost, for we have a stout-hearted guide to lead us through the coming darkness; a strong, inspiring, practical woman, who won't let the little matter of nuclear Armageddon disrupt her well-ordered life. Or at least… she seems to see it that way.

The woman in question is Lotta Quizeen, the long-time alter ego of performer Katie Richardson, whose Thatcheresque imperiousness and love of domestic regimen make her the ideal candidate to organise a brave new world underground. She has roles in mind for all of us, and she's stockpiled plenty of cake mix; and if this all seems a touch gender-stereotyped for your taste, don't worry, she's sorted out the generator too. But her son Hugo's been out on patrol, and he's really quite late returning. He'll be all right, of course. He's just a bit delayed. Isn't he?

The story that follows is cleverly constructed, with hints of something even darker than nuclear winter poking at the edges of Lotta's mind. Unexplained motifs – from her obsession with the wild dogs hunting outside, to her out-of-place musings on forgiveness – together suggest there's something about Lotta's recent history which she isn't quite letting on. By the end, when it's all snapped into place, we have a renewed understanding of how she came to be in this bunker, and of what life after the bomb went off might actually mean to her.

Tonally though, there's something slightly jarring. At points, Lotta segues from being a brisk no-nonsense matron into a post-apocalyptic parody of a game-show host – a joke which is funny enough to pass muster, but which doesn't quite fit the overall trajectory of her story. And the time consumed by those segments is time that can't be spent exploring Lotta's many-layered personality, with the result that the ending – though clever and affecting – isn't quite the gut-wrench that it could be.

Not all immersive shows have to be interactive, and here the audience participation feels a little shoehorned-in. But it's a fitting next chapter to Lotta's ongoing story, and despite the sharp downward turn the world around her has taken, she has a curiously upbeat message to give us at the end. It's the end of the world as she knows it, and she doesn't feel fine. But however bad the circumstances, she can – we can – find the strength to keep calm and carry on.