David Mitchell was born to play Ludwig who's half man, half corduroy

Sometimes a new series arrives and instantly just feels so right. Comedy drama Ludwig is one of those pearls that pops out perfectly formed. David Mitchell is immaculately cast as John Taylor, a bookish puzzle setter whose nom de plume is Ludwig, because, as we discover in episode one, he has a thing about Beethoven dating back to childhood.

Ludwig episode 1 recap
Ludwig episode 2 recap
Luwdwig episode 3 recap
Ludwig cast

But a programme about a middle-aged man sitting alone creating crosswords might not have much comedy or drama, so writer Mark Brotherhood has come up with a fiendish storyline to add some jeopardy. Emotionally detached John's identical twin brother James, a high-flying police officer in Cambridge, has inexplicably disappeared and James's wife Lucy ( Anna Maxwell Martin ) needs John to help her solve this real-life conundrum.

It should be simple. All John has to do is pop into the police station impersonating James and pick up his notebook. But, before you can say Midsomer Murders there's a dead body and John/James has been landed with a case to crack…

Don't scrutinise the plot too closely or Ludwig will quickly unravel. Is everyone in the police station so poor at spotting clues none of them realise that he is not James? There are some curious glances from DI Carter (Dipo Ola) who wonders why "James" has parked his Saab so badly but he seems to accept new contact lenses as an explanation.

It's a wonder then then this force can find the milk to go in their tea with those observational skills. But, guess what, John turns out to be a brilliant crime buster, treating the investigation as another logic brainteaser to be solved. Like a tie-wearing Miss Marple, he swiftly does their job for them.

The speed of his detection leaves plenty of room for some backstory. The twins’ father walked out on his family in 1989. Both sons were traumatised, but while James coped by being open and extrovert, bullied and bookish John shut down, preferring his own company and the safety of his study. Will this new turn of events bring John out of his shell? Well, it won’t be much of a comedic case-of-the-week series if it doesn’t.

A hugely enjoyable script also finds time to plant some intriguing hints about what might come next. Is it possible that John has been in love with Lucy but could not act on it while she was happily married? Is there something sinister going on at police HQ? Is there more to Chief Constable Ziegler (Ralph Ineson) than meets the eye? And why does Holly ( Alma's Not Normal 's Sophie Willan swapping red hair for black bob) keep giving John funny looks?

Needless to say, Mitchell looks as if he was born to play John, half man, half corduroy, with some tweed and a pocketful of pencils thrown in for good measure. Somehow this feels both engagingly original and reassuringly formulaic. If you were a fan of Mitchell's breakout sitcom Peep Show you don’t have to squint very hard to imagine that John is Peep Show ’s Mark two decades and one greying beard later. I wonder if he will pop up as James in future episodes though. That might be more of an acting challenge.

It is to the programme’s credit that they have avoided TV cliches and haven’t lumbered Ludwig with a limp, a vintage car or a faithful dog. OK, he might be a stickler for routine (if it's Sunday it must be carbonara) and he might be overly fussy about detail but that turns out to be as useful for villain-detecting as it is for crossword-devising.

Agatha Christie fan Mitchell himself has described Ludwig as "cosy" and this is certainly a world away from recent grisly thrillers. It is one to watch with a mug of cocoa rather than a bottle of tequila. It might be about violent culprits but it makes you smile when you think about it rather than rush to double-bolt your front door.

Maybe it is at the forefront of a trend for more gentle cop TV after the serious grittiness of the likes of Luther , Line Of Duty and Sherwood . By coincidence, Timothy Spall has recently been filming Death Valley , a new BBC comedy drama set in Wales in which he plays an actor who once played a TV investigator finding himself investigating a neighbourhood killing.

Perhaps it is all Richard Osman 's fault. His Thursday Murder Club best-sellers have shown that the business of catching killers can sometimes be quite a sedate affair. Shooting has just wrapped on the Netflix-bound movie version of his debut novel starring Helen Mirren, Pierce Brosnan and Ben Kingsley as the senior citizen sleuths.

But I digress. I should be more like Ludwig and stick to the subject at hand. There's lots to like about this new series, from the elegant shots of Cambridge (where, of course, Mitchell studied in real life) to the chemistry and interplay between Lucy and John. Could their friendship turn into something more? It would be criminal not to keep watching to find out.

Ludwig is on BBC One on Wednesdays at 9 pm. The full series is available on iPlayer.