In Richard Holloway’s book Waiting for the Last Bus – it’s about dying – he peers into the existential abyss. “The experiment of being was empty of meaning from the beginning,” he writes, “and the universe is destined to be sucked back into the nothingness it came from.” All our striving, all our thought, art and achievement – perhaps even our comedy – is ultimately meaningless. So how should we live? “Even if it is nothingness that awaits us and the universe,” he concludes, rather beautifully, “we humans should so live that that will be an unjust fate.”

Which brings us to Brexit – the apocalypse in microcosm – and to satire. In the run-up to what is no longer “Brexit Day”, Andy Zaltzman is presenting three tailored editions of his Satirist for Hire show, a format that offers “bespoke on-demand satire” in response to audience requests emailed in advance. Zaltzman kickstarts proceedings with a question of his own: “Can satire help?” He doubts it. “Mock the Week’s been on TV for 16 years now – and look at Syria!” Satire, according to this satirist for hire – and in agreement with fellow political comic Andy Parsons on his last tour – is impotent. Adjust your expectations accordingly.

I duly did so, and enjoyed the show, while wishing now and then that Zaltzman would perform as if satire’s ultimate meaninglessness were an unjust fate. But he seems to be at peace with it. He’s here not to change the world, nor even try to, but to make us laugh. Which he does from the off, mocking the idea – in a country with a first past the post electoral system, an unelected upper house and a monarchy – that a second referendum would undermine democracy. (“Undermining democracy is hardwired into our national psyche…”)

‘Can satire help? Mock the Week’s been on TV for 16 years and look at Syria!’ Photograph: BBC/Angst Productions/Ken McKay

That’s just the first of plenty of good Brexit gags tonight, few of which have much to do with the prompts given to Zaltzman by his audience. The dictionary is deployed to throw well-deserved shade on the phrase “leave means leave”, while another gag turns our doomed PM’s “citizens of nowhere” jibe drolly against her. His proposed third option on the EU referendum ballot paper is obvious but amusingly expressed, and there’s a nerdy and novel routine on the historical significance of 29 March.

In response to a straw poll of his audience’s Brexit affiliations, Zaltzman quips at the start that his show is taking place inside the most remainer-y of bubbles. But there’s not much here that a leaver couldn’t enjoy. Our host wisecracks about his own ambivalence towards Brexit – which is bad for his kids, and good for his comedy. The butt of the humour isn’t Brexit itself, usually, but the pig’s ear that’s been made of it. And the jokes, while often clever, are very mild mannered. They’re animated less by partisanship or depth of feeling than by jaunty delight in their own amusingness.

Anything more ardent wouldn’t be Zaltzman’s style. It wouldn’t be cricket, in short – cricket being Zaltzman’s first love, and that of many of his fans. Several of his correspondents tonight pose questions on the subject, which arouse more fervour in our host than anything to do with Brexit. When it comes to the politics, there’s not even the pretence that the show might change minds, scourge the powerful or reveal things in a radical new light.

In lieu of all that, we get an entertaining hour of comedy, which never stints on urbane humour, showcases some deft ad-libs and puts Zaltzman’s easy bonhomie with a home crowd to good use. But beyond that, it does little to redeem satire’s beleaguered reputation. Of course, comedy’s primary job is to make us laugh. And yes, it can be hard – especially at times like these – to keep believing it might make the slightest difference in the world. But I like my satirists to defy futility, not cheerfully accept it. To live as if – pace Holloway – their meaninglessness were not just an injustice but a mortal affront.