Evil has never been so banal. Running capital punishment through the wringer of office politics, Toby Whithouse's comic monologue shows just how easily authoritarianism entrenches itself into everyday life. It hides behind inane protocol and pecking orders until it's practically invisible to the naked eye: waved through by a thousand jobsworth dogsbodies.

Dogsbodies like Ian: a man who puts the anal into "banality of evil." A hangman holding out for a big promotion at work, he's basically Hannah Arendt's worst nightmare: the yessiest of yes men. His pride in the job would be quite touching were his job any different.

Positing a Britain that reinstated capital punishment in 1975 off the back of - what else? - a referendum, Whithouse tracks forwards 40-odd years until executions have become commonplace. It's the old Amber Rudd argument: If you've done nothing wrong, you've nothing to fear. The issue with that, clearly is mission creep, and a system that had 75 per cent approval ratings to start with, has seen it's ratings go up over time. "Dissent had its chance," offers Ian, innocently. Do you look down on dustmen, Ian asks. "Only it's the same job."

In those terms, executions lose their extremity. Capital punishment stops being a question and instead becomes a system - either efficient or not, but never up for grabs. Whithouse nails the way evil hides in plain sight - and you can't help but wonder what evils we ourselves are overlooking. Ian's open to the point of obsessiveness, measuring people up for the drop the moment he meets them. At the same time, such death has lost its sting. It's wrapped up in two-day courses and team building exercises, who gets what office and jokes on repeat. "Come on," he says to new recruits, "I'll show you the ropes."

At times, Executioner Number One is closer to character comedy than drama. Ian is his own material and Whithouse nails a very particular breed of Brit - pernickety, self-important and oh-so suburban. A small fish in a smaller pond. It's perfect sitcom stock. Imagine Gordon Brittas running a pogrom. Gareth Keenan at the helm of the SS; Assistant to the Minister for Propaganda. His plain black suit hangs loose at his sides. His parting's slicked down and his trim pencil moustache sits, just so, over lips that purse into the most shit-eating smile. Good God, he's punchable. Smug. Penny-pinching. Gutless.

At times, Ian embodies the blimpish nostalgia that has gripped this country of late. He pines after a simpler world and refuses to move with the times. When his own deputy emerges as a rival candidate, eloquently advocating a programme of painless gas-based executions, Ian insists that death must be its own deterrent. There are echoes of our own politics in that. The dates are key - 1975 being the inception of Thatcherism and the deputy's proposals, compassionate capital punishment, are as self-defeating as New Labour's neoliberalism. Both leave little room for alternatives.

There is, then, more to Executioner Number One than its comic veneer. Though it never lands its stomach punches, the writing leaves a sour aftertaste. It zooms in from impersonal system to lived experience, as Ian fixates on a moment that marked him – the botched execution of a boy sentenced for his part in a police officer's death.

Suddenly, Whithouse's writing sticks in the throat and Ian's exacting nature comes into its own. Fastidious details, once humorous, become quietly horrifying: weight, duration, length of rope. "Your priority is the maths," he says, but numbers can't conceal everything. The point is it takes a glitch to see a system for what it really is and it's only with something going wrong that we clock our own culpability. By then, it's too late.

Executioner Number One runs at the Soho Theatre until 15 April.