Greg Davies is the biggest thing in comedy right now – if only in a literal sense. “I’m technically a giant,” the colossal comic notes, while discussing the advantages of a mountainous physique in his chosen profession. “I didn’t start comedy till I was 33 years of age, and I’d say it was the first time in my life that my height has benefited me. Throughout my youth, it just made me feel self-conscious and set me up for criticism, because I was always rubbish at sport and short people have always been very annoyed at me for being bad at sport with a big body.”

Once he pursued a comedy career, though, Davies found, as myriad tall comedians have before him, that size mattered. It came in handy when playing hate-filled teacher Mr Gilbert in The Inbetweeners, the massive discrepancy between his height (2.03 metres) and that of the students beneath him highlighting the power imbalance. It also comes in handy in his role as himself on Taskmaster, where he sits in judgment on hapless panels of comedians forced to perform bizarrely complex and pointless tasks at the big man’s bidding. The ability to play the authority figure – and to skilfully subvert the expectations attached to it – has been a hallmark of Davies’s career thus far. His latest endeavour, however, is something a little bit different.

In The Cleaner, Davies plays Wicky, a crime-scene cleaner who arrives after gruesome deeds have been done to mop up the stomach-churning residue, and in the process encounters a variety of characters ranging from the eccentric to the downright terrifying. Does the show – also written by Davies – reveal a deep fascination with death? “I’ve had an obsession with death my whole life, that I can’t quite explain,” he admits. “So I do feel there was an element of destiny to The Cleaner arriving at my doorstep. I’ve always been obsessed with mortality, but not in any profound way – I just can’t quite get my head around it.”

It’s the perfect attitude for Wicky, for whom not quite getting his head around things is a regular experience, constantly confronting the unfamiliar and trying to process it. Wicky is no authority figure – in fact he is frequently affronted by people considering him a menial worker – but the character is one that fits Davies like a glove, allowing him to play the part of an ordinary man dealing with the extraordinary. It’s no doubt his talent for inhabiting the everyman – height notwithstanding – that convinced producers he was the man to go to when adapting the successful German sitcom Der Tatortreiniger (“the crime scene cleaner”).

“He’s someone who has very simplistic needs in life,” Davies says of Wicky. “That’s part of the brilliance of the original format: that rather than putting a very troubled, dark soul into these bizarre situations, you’ve got quite an ordinary bloke who just likes going to the pub every Friday. That’s quite a juxtaposition with the characters he meets. The characters he meets are absolutely bonkers, but he remains straightforward and responding to really mad characters in a quite sensible way. He’s quite sensible in many ways, quite moralistic.”

Just as Davies was engaged by the ordinariness of the character, it was the mundane side of the job of crime-scene cleaning, rather than its grislier aspects, that most fascinated him. “One of the most interesting things about the job is how boring it can be at times. It is a very specialised profession, but a lot of it is just graft, it is the graft of cleaning. It’s no more glamorous than if you spilt a casserole on the floor: you have to just get down, throw towels down and get the worst of it up, as my mum would say. So that’s the thing I found most interesting: they get parachuted into these extraordinary situations but a lot of the time they’re doing humdrum cleaning work.”

The Cleaner is all about juxtapositions: between shocking crimes and tedious cleaning, or between Wicky and whatever oddball he’s come across today. Each episode is, for the most part, a two-hander, Davies playing opposite an impressive array of guest stars, including David Mitchell, Stephanie Cole and Helena Bonham Carter. For any actor the chance to go head-to-head with another major talent for half an hour has to be a thrill. “It feels like such a treat,” Davies confirms. “I love it, because it means you have the chance to form a meaningful relationship with that person in half an hour. It’s really exciting to just play against one person and feel that you do, at least a little bit, get under the skin of the character. It’s very old-fashioned, really – in the ’70s and ’80s there was a show on the BBC called Play for Today, which was a play transposed onto TV. I feel it’s a bit like that.”