Brexit is impossible to escape, but equally impossible to fully grasp. However, the likely practical consequences of Britain leaving the EU have, arguably, been underexplored on non-news TV. Perhaps that’s down to the sense of impotence the subject induces: the period since the referendum has felt like looking on helplessly as a toddler prepares to stick a fork in a plug socket.

In British Workers Wanted (16 November, 10pm, Channel 4), someone finally goes there. “There” in this case, is Bognor Regis, home to Sarah (good cop) and Gaynor (permanently enraged cop), two leave-voting ladies who run the recruitment agency Opus Loco. It’s also currently home to many eastern Europeans – a staggering 98% of their employees, in fact. Already, Opus Loco’s steadiest workers are drifting away, leaving them with what’s portrayed in this doc as an apathetic rump of graft-averse, late-arriving, illness-feigning, indigenous Brits.

In fairness – and it’s an issue that lamentably isn’t much explored here – most of these jobs are poorly paid and, for the most part, entirely insecure, even from one week to the next. Even so, a few Brits are placed in work. Andre, for example, does his best. A few hours after he starts, Sarah checks in with his new boss. Might they want Andre for next week, too? “Is Oleg about?” comes the plaintive, telling reply.

Strong and stable ... the Opus Loco team. Photograph: Richard Ansett

But Sarah and Gaynor are nothing if not optimists. They recruit Michael to join their office team. He’s a cheerful, handsome lad, whom they imagine will be able to communicate with Bognor’s youth on their behalf and thus help fill a staffing hole that is beginning to gape like the Grand Canyon. With a large event at Goodwood upcoming, they launch a poster campaign and host a networking evening that achieves, as Sarah puts it, “absolutely bollock all”. Soon, Gaynor loses patience with Michael, whose unwavering commitment to fag breaks, Facebook and selfies isn’t quite matched by his work ethic. Crisis point is reached. Fortunately, there are still a few Latvians to pick up the slack. For now.

The tone becomes increasingly uneasy: for light relief, we take detours into Sarah’s online dating experiences, and the film is soundtracked by the kind of twee, jaunty music that’s customarily used to accompany films about competitive shed-building or some such Great British quirkiness. In the context of a programme that’s essentially A Very British Gig Economy Staffing Crisis, it starts to feel demented. Because it’s window dressing. This film is profoundly dispiriting. Everything about it – the wages, the conditions, the way Gaynor talks about the prospective staff (“Some fucking twat”) – radiates bad faith.

There are many British people – and it isn’t a stretch to imagine that Gaynor might be among them – who posit Brexit as a tough-love elixir for feckless, lazy locals. Indeed, Gaynor reaffirms her commitment to Brexit at the end of the film. Sarah, though, would now vote to remain in the EU. “We were misinformed,” she reckons. “Don’t tell Gaynor I said that.” But Gaynor and Sarah will have to have this conversation soon. As will many of us. In the meantime, at least British Workers Wanted offers a hint about why programmes about the specifics of Brexit are so few and far between. It’s not a mirror we’re all that keen to look into just yet. But the clock is ticking.