Rob Delaney’s been a British resident since his sitcom Catastrophe took off – and this country seems like the right home for him. For the comic is the antithesis of stereotypical American pep, instead being hard-wired to expect the worst from life – an attitude far more typical of these grey, rain-lashed isles.

Yet in his new Amazon Prime special, Jackie, he is one of the most cheery world-weary cynics you would hope to encounter. Having resigned himself to the futility and grinding disappointment of existence, he finds glee in its absurdities.

Broadly speaking, his shtick is of a useless schlub of a man: lazy, judgmental, immature and embarrassing to those around him – even though he’s acutely aware of all those failings. In that, he’s like a Louis CK it’s still OK to enjoy.

Delaney is a fully signed-up liberal, mind. There’s an endearing tale of when he tells his delighted young sons that men can marry men, he sings the praises of the NHS (applause-fodder, maybe, but it’s sincere), and more darkly finds glee in imagining the out-of-shape Donald Trump dying in front of his sons, who battle in vain to save him. Such are the images that cheer him up.

Delaney’s evident affection for his children counters the innate misanthropy, with dark and light clashing as he teaches them about the brutal realities of life. Such moments have added poignancy in light of his recent family tragedy, but that raw subject is not something chooses to raise here.

Being woke and trying to be a decent dad doesn’t put him above making dick jokes, however, with the memorable description of his awful penis one of the hour’s funniest segments.

Sometimes he confronts his failings head-on, with the story of his drink-driving accident and subsequent conviction, 17 years ago, proving both heartfelt and hilarious. Other times he states his less empathetic ideas – from needing help reading his wife’s mood to giving his sons the graphic details of how their pet (Jackie) might have died – and lets us laugh at what sort of unreconstructed asshole would think of such things. 

But however much of dick he’s being in his stories, there’s an understanding that it’s exaggerated. And as if to underline that he’s one of the good guys, he ends by recounting a creepy encounter with Bill Cosby from long before his crimes were known that will turn your stomach.

As well as informing the tone of the show, Delaney’s British sensibilities are on display in the execution. These are not slick, precision-honed routines; instead, the anecdotes tumble out of him like loose but excited conversations. Witness how many sentences start ‘And…’ as he rushes through the thoughts he has to get out. That gives the show a casual intimacy that helps the storytelling, but perhaps at the expense of highly-polished punchlines that pop in an explosion of laughter.

But he’s a charismatic, naturally funny, teller of tales, whose self-deprecating, and counterintuitively life-affirming, anecdotes will lighten up the hour you spend with him.

• Rob Delaney: Jackie is available on Amazon Prime now.