Always use a condom, kids. The underlying message comes through loud and clear from new BBC Three sitcom Daddy Issues, which delivers a potent blend of wit and charm about its pregnant young heroine throughout its six episodes, without ever losing sight of the fact that life would have been much better if she had managed to avoid getting into such a predicament in the first place.

Aimee Lou Wood, whose comedy credentials have been in no doubt since her screen debut in Sex Education five years ago, plays Gemma, a 24-year-old Stockport hairdresser. Gemma likes partying and hooking up, until one bareback encounter in a plane toilet with a man who can’t even quote famous TV adverts correctly (such a perfect skewering of the very last type you want fathering your child) leaves her up the duff.

That would be a problem even if her flatmate hadn’t just left her in the lurch, if her mother Davina (Susan Lynch) hadn’t recently buggered off to foreign parts with a new boyfriend, and her sister Catherine (a wonderful turn from My Mad Fat Diary’s Sharon Rooney) wasn’t in prison for trying to have her boyfriend killed for the life insurance (“How can it be a crime if you fail?”). Oh, and she’s also lost touch with most of her friends over the years and her dad Malcolm is a beaten beta living in a bedsit whose bathroom facilities are shared with five other men while he tries to recover from his wife’s desertion and master the basic life skills he has never needed to acquire. He is played, against type, by David Morrissey, whose comedic gifts may not outweigh his dramatic talents, but whose ability to make anything and anyone credible carries him through proceedings with aplomb.

The other principal characters are : Cherry (Taj Atwal), a one-time school friend and now single mother of two with whom Gemma reconnects in desperation; Derek (David Fynn), a borderline incel who is Malcolm’s landlord and forcibly befriends him, becoming as Gemma puts it “your emotional support dickhead”; Rita (Sarah Hadland), Gemma’s equally hard-partying boss, whose ambitions for a career in espionage were scuppered when she “sucked off Mike Baldwin on a Coronation Street tour” – even though “they” didn’t realise she’d done Kevin Webster, too; and sweet, gentle pharmacist Xander (Arian Nik), who is gradually moving from the periphery of Gemma’s life to a potentially more central role. A love interest who knows you by your UTI prescriptions first is a keeper, in my opinion.

To save herself from homelessness, and Malcolm from starvation and/or cholera, Gemma takes her dad on as her new flatmate. This very modern odd-couple arrangement allows them both to survive – if not quite thrive – and the two stars to showcase their chemistry and give us an increasingly touching portrait of a fractured relationship slowly mending. The show is writer Danielle Ward’s solo creation and one of its finest points (alongside the men who keep smuggling things up their bums into Catherine’s prison simply because they like it: “I don’t even need a new vape pen” sighs a fellow jailbird) is that Malcolm’s domestic incompetencies aren’t played solely for laughs but to add to Gemma’s daily burdens. It’s hard not to warm to a show that gives emotional and invisible labour its infuriating due.

High jinks elsewhere abound, of course, to take care of the sitcom’s “com” as Gemma tries to cope with her pregnancy, snare a sugar daddy (the only bearable candidate proves to be a conspiracy theorist), keep up with the rent, and forge some sort of support network around her. Malcolm learns not to mop up bin juice with his jacket, joins a boxing club for depressed men, and tries to get himself out on the dating scene again. He’s not really ready. “Davina was cruel, but at least I knew where her bits were and how they worked. She was like a menopausal Ford Focus,” he explains earnestly to his emotional support dickhead.

Daddy Issues is daft, honest, funny and tinged with bleakness (the sight of Wood’s innately childlike face so wearied in almost every scene is a perfect emblem of the whole). It gives stereotypes a twist – Derek, for example, is just that bit more vicious than the traditional sitcom sexist is normally allowed to be – and everything feels that bit more resonant as a result. You will laugh, but you might also cry. Or at least find yourself staring at the wall, having a think and sighing very deeply before you go on with your day. A comedy for our times.