Ol’ Blue Eyes is back: first staged in Birmingham three years ago and workshopped since, this Frank Sinatra bio-musical has now hit the West End with big band energy. Its intriguing premise is the star’s nadir, those messy years in the late 40s and early 50s when it seemed like an extraordinary talent might come to a wasteful, tragic end.

We begin at the Paramount theatre, when our heart-throb has everything going for him: screaming fans, a devoted spaghetti-cooking spouse, a movie about sailors with Gene Kelly that’s going to deal with the pesky accusations of draft-dodging. In the lead, Joel Harper-Jackson marries smooth vocal power to Sinatra’s signature swagger – the head wobble, the corner-of-the-mouth smirk. Our hero’s weakness for women is played as a comically charming character quirk, with a bed-hopping rendition of Come Fly With Me involving Lana Turner, Judy Garland and Marlene Dietrich.

When Sinatra meets Ava Gardner in Palm Springs, he soon has her under his skin and it’s the beginning of the end for his marriage to Nancy (Phoebe Panaretos). But while Ana Villafañe captures Gardner’s bombshell power, and there’s no lack of passion in the musical numbers, Joe DiPietro’s book never spirits up the true tumult of this legendary affair. This is a couple whose first date allegedly ended in drunken gunplay, but the febrile nature of their relationship is here limited to a ceremonious smashing of whisky glasses in a grate.

Sinatra’s producer daughter Tina, who helped shape the story, wanted her father to be better understood. But a reluctance to embrace too much darkness lends a sense that things just happen to our hero. It’s at odds with the comeback narrative and the stubbornness we’re told he’s inherited from his Italian mother – Jenna Russell, who can steal a scene with just a single line delivered on a telephone.

We do get some colouring in on Sinatra’s progressive values, and the sense of anti-immigrant discrimination that drove him, but the script often feels less three-dimensional than the video-assisted set design. Happily, Kathleen Marshall’s production, complete with a fine ensemble and some joyful choreography, doesn’t stint on the big hits – on opening night you could literally hear the audience swoon.