The year is 1929. A time for Americans to stand knee-deep in spooling ticker tape and wail “What gives?” A time for Helen McCrory as Aunt Polly to untangle herself from her lover in a Monte Carlo hotel suite, rearrange her furs, pout to emphasise her peerless cheekbones and head back to Small Heath for a family crisis meeting. A time for Arthur Shelby to swig from the bottle and sob over the Detroit wing of the crime mob failing to ditch their stocks before they became worthless.

It is time, in other words, for season five of Peaky Blinders (BBC One), the franchise that does what Amy Turtle from Crossroads could never manage – to make fans as unlikely as Snoop Dogg realise that the important Birmingham isn’t the one in Alabama.

Good news, Mr Dogg: the formula is the same. Sharp duds that reprove today’s sartorial slobathon? Check. Caps that allow middle-aged chumps like me to feel ancestral connection with their great-grandads? Check. Gaudy, exploitative violence? Sure. The six-abreast Reservoir Dogs strut across cobbles, backlit by factory flames? But of course. Cillian Murphy as mob boss Tommy Shelby in existential crisis like Tony Soprano? Oh, go on then.

Like Ronnie Barker in the sequel to Porridge, or Michael Corleone in The Godfather Pt III, Tommy wants to go straight but keeps getting dragged back in to the moral cesspit he dug in the first place.

And the accents. My God, the accents. Is there a compulsory Rada course in Brummie for disappointed poshos hoping to spend their careers deploying Jane Austen cleavages and skinny breeches, but instead are forced to watch Timothy Spall in Auf Wiedersehen, Pet, and Harry Enfield as second city parvenu? “Repeat after me,” says the teacher, “Oi am considerably richer than yow”. Let’s be thankful: at least dead horses don’t talk. Not that I’m complaining: the pleasure of watching period drama is pointing out its shortcomings.

What can the Peaky Blinders do to avoid catching a cold from Wall Street’s sneeze? That was the question of this series opener. Tommy has a lot of thinking to do. So he saddles up, like a Clint Eastwood who has swapped poncho and Stetson for starched collar and flat cap. He trots moodily on another horse across the wild West Midlands in fetching silhouette to the soundtrack of Nick Cave at his most risibly bleak. He is heading for them thar Lickey Hills. I used to sledge down those hills as a kid and don’t recall a phone box on top, less one that worked. But this one does. What’s more, it’s ringing.

Who is on the other end of the line? Tommy gets off his horse to find out. One of his lackeys explains that Limehouse gangsters won’t surrender the compromising poop on a peer of the realm that Tommy has been offered £50,000 to retrieve. So he orders a hit to save face. Cut to the Peaky Blinders blasting their way into the gangsters’ HQ. Limehouse’s error? They expected the Brummies to come though the door. Instead, they shot their way through the walls, emerging covered in plaster, as implacable and savage as escaped lions from West Midlands safari park.

Like a Brummie Zelig, Tommy is everywhere. The series creator Steven Knight is heroic, perhaps even heroically misguided, in having no compunctions about making his hero have fingers in every pie going. Ordering hits in Chinatown. Receiving letters from Winston Churchill. Sobbing graveside over a horse interred by Gypsy chums. He has even become a Labour MP, although when it comes to representing Birmingham, he is no Jess Phillips.

He is so little a man of principle, in fact, that when Sam Claflin’s Oswald Mosley, who formed the British Union of Fascists in 1932, slimes out of his office in the Palace of Westminster to get Shelby on side (yet another Zelig-like coincidence), we wonder: who would Tommy fight for in the looming battle of Cable Street – for the fascists, or against?

All this was daft enough, but then Knight crossed the line. He killed off a reporter in the line of duty. If you have flat caps to doff, doff them now. Michael Levitt was killed for knowing too much. What did Levitt know? That Tommy is a killer by remote control and his dabs are all over the crimes. The Peaky Blinders waste Levitt in his apartment block lift, feathers from the lift’s upholstered walls fancifully fluttering in the air as his corpse slips to the floor.

You can put your caps back on now. Clearly Levitt was a phoney. He never worked for the Evening Mail, really. Instead he was an implausible invention, played by a graduate from another Rada course, Telly Journalists 101, that teaches the following: on no account take a shorthand note, stare sweatily at your unused notepad and then get rubbed out for asking the difficult questions. Poor show.