Half an hour, minus the ad break, isn’t long to establish character, sketch a plot and pump an audience full of gags, but Sharon Horgan and Rob Delaney ring all three bells in Catastrophe (Channel 4).

Horgan was responsible for BBC3’s criminally dumped Pulling (along with Dennis Kelly) and US standup Delaney rose to fame in Britain via Twitter, collecting more than a million followers with his sordid but uproarious tales of former addiction. In Catastrophe, they play versions of themselves, in that they’re called Sharon and Rob and share some backstory with their characters, but she is a London teacher and he is a nonspecific businessperson in New York.

This opener rattles along like a flicker book or zoetrope, from their meet-cute straight to the button-popping sex and then, just as swiftly, to their parting when Rob flies back to the States. Four minutes and 18 seconds in, it’s all over. Sharon and Rob have gone their separate ways, agreeing it was a fling. He leaves without so much as a sentimental airport parting, just a final pre-flight bunk-up in a stairwell.

Despite the perfunctory nature of all this urgent humping, the romance leaks through in the obvious chemistry between Horgan and Delaney. On parting, he describes her as “an extraordinarily good-smelling woman with a magical ass”, and she reciprocates, saying he is a “sturdy love-maker with a massive chin”.

They underplay the growing affection perfectly, without the cloying sentimentality you’d think they would need to make the next bit work. And the next bit is tricky.

While dining with a date back in New York, Rob gets the call from, as his phone has her listed, “Sharon – London (sex)”, that will propel the plot from here on in. She is pregnant. And because you already believe there are feelings at play, despite all the sizzling one-liners, it justifies the sizable leap you’re now asked to take. Rob flies to England to “figure this out” and they agree, indecently quickly, to have a baby with each other, based on a week of furious rutting and some shared banter.

The decision happens during a scene on a bench in Kew Gardens, and again there is no teary angst giving way to sticky sentimentality, accompanied by heartfelt piano. Their crisp to-and-fro outlines the problem and the quickly reached solution in a tone in keeping with episode’s breakneck pace. “Who says I’m keeping it?” mutters Sharon. And that’s the looming spectre of abortion dealt with. But in this context, it completely works.

They’d whipped me up into such a frenzy by that point with the nimble dialogue and surprisingly high gag-rate, I was a skimming stone, bouncing across the pond of their narrative. Why put the brakes on now when I want to know what happens next?

And praise be, after scores of British sitcoms based around the nonspecific, warm, fuzzy feeling generated by people being kind at each other, a half hour of narrative comedy that bursts with jokes. Solid, delicious chunks of funny pudding rather than the funny-flavoured foam we’ve been doused in lately. Some depravity, lots of misdirection, a little embarrassment; they don’t favour one particular style. The scenes between them come across as verbal tennis matches, like Hildy and Walt in His Girl Friday, but less shrill.

Their two senses of humour are distinct if you’ve seen Horgan’s previous work (and you should) or followed Delaney on Twitter, or watched one of his eye-popping live sets. But together they have a direct link to the same cesspool of unabashed human self-loathing that feeds the laughs. There’s a real honesty about his standup, and what a mess he was before sobering up, that marries well with Horgan’s sometimes confessional comedy, acknowledging the parts of her personality she doesn’t like. Selfish, vain Donna in Pulling was Horgan’s avatar in the same way David Brent was for Ricky Gervais.

“She seems nice,” says Rob of Sharon’s plainly toxic friend Fran, a homeopath played with relish by Ashley Jensen. “She’s a cunt,” Sharon shoots back. Commercial break. The pace is sure and brisk without losing emotion, takes real skill. As their relationship develops, so does ours with them.

Horgan cheerfully leaks some of the inner darkness lurking in Sharon when she wishes Fran’s dad would get caught with child porn “just to knock the smug out of her”. Rob grins when, during their first meeting, he admits he gave up booze after soiling his pants at his sister’s wedding.

For all this degeneracy, it isn’t plain dark or out to shock. It’s genuinely sweet and I care what happens to them. Just not the kind of sweet that gets stuck in your teeth.