There’s an age-old stereotype that Germans don’t have much taste for comedy, but Greg Davies clearly doesn’t agree. For his new BBC One sitcom, the Taskmaster star has adapted the long-running German series Der Tatortreiniger, which revolves around a proud crime scene cleaner and the various eccentrics he encounters while carrying out his rather grisly job. It’s an intriguing concept, and one with lots of opportunity for the blackest of black humour, but for the most part the format is wasted in this remake in favour of relatively tired gags and unfunny references to things like “the tattooed milf.”

Davies stars as the titular cleaner, Paul ‘Wicky’ Wickstead, a middle-aged man who takes great pride in his job but whose personal life is somewhat in a state of arrested development (his main goal in life is to finish his job quickly enough to make curry night at the local boozer). The character’s schtick isn’t too much of a diversion from Davies’ usual comic persona – he’s a little world-weary and he suffers no fools – and Davies is a likeable enough presence to just about pull it off, even if most of his trademark rants lack the hilarity we’ve seen in his stand-up and panel show appearances.

Probably the biggest draw of the series is the starry supporting cast that Davies has managed to assemble, with each individual episode revolving around Wicky’s interactions with a different guest star – whether that be David Mitchell’s pedantic and frustrated author or Layton Williams’s shallow and self-interested influencer. This structure allows each episode to explore different themes and issues as Wicky inevitably gets drawn into conversation with the assorted characters, but it also means that the instalments differ wildly in quality – from the really quite poor to the fairly enjoyable.

The biggest star of all, Helena Bonham Carter, appears in the first of the six episodes – playing a widow who brutally murders her husband after growing tired of his control-freak ways. The episode sees her hold Wicky captive inside her house when she makes a surprise re-entrance, with much of the ensuing drama taking place inside the bathroom, where she insists Wicky stays at all times.

There’s no doubting Bonham Carter’s star quality, and she commits to the bit, but I found this episode to be a major disappointment. There’s plenty of disbelieving back and forth between the two characters as the widow explains the reasons for offing her husband, and there’s an abundance of crude jokes, but the humour never really gels and it all ends up coming off a little forced. That the episode’s finest moment is a fantasy sequence in which the pair sing a duet of Frank Sinatra’s It Had To Be You while Bonham Carter is sat on the toilet probably tells you everything you need to know.

The better episodes are the ones where the humour actually takes more of a backseat. My favourite of the bunch was episode four, titled The Aristocrat, which sees Wicky despatched to the opulent mansion of a snobbish old lady (Stephanie Cole) who was recently the target of a failed burglary attempt. The tone here is still comic, of course, but there’s a little suspense thrown in as well as Wicky begins to realise there’s more to the case than meets the eye and finds himself facing something of a moral dilemma. This gives the episode a sense of narrative drive that some of the other instalments lack, and ensures it becomes an altogether more engaging experience.

There’s something of Inside No. 9 to the series – they’re both darkly comic anthology shows that largely take place in single contained locations – but the scripts here just aren’t as sharp or original as in Reece Shearsmith and Steve Pemberton’s terrific series, meaning The Cleaner isn’t as dark or as comic as it needs to be to go down as an unqualified success.

The show is still plenty watchable – you can tell that directors Tom Mitchell and Alex Winckler had fun constructing some of the gory cleaning montage sequences, while there’s a certain amount of enjoyment to be had watching the guest stars do their thing (David Mitchell, in particular, is perfectly cast) – but on the whole, this is a series that just doesn’t quite live up to its potential.