The offstage moments are the glories of “Judy,” the places where Renée Zellweger truly inhabits the child star turned showbiz legend, a shell of her former self in the last year of her life. It’s all the stuff ON-stage that lets the picture down.

Zellweger and the script — based on a play by Peter Quilter — make Judy Garland a sad and lonely figure, not a tragic one. She is managing, rolling with the punches of an expensive divorce from Sid Luft (Rufus Sewell, playing a man exhausted by her), nearly broke and essentially homeless — if life in hotel suites, where sometimes she couldn’t pay the bills, counts as “homeless.” She is drinking, clinging to her lifelong, studio-mandated regimen of uppers and downers, regal, plucky and self-aware.

She knows she’s a star, a legend even. When she joins daughter Liza Minnelli (Gemma-Leah Devereux, with just the right spark) at an L.A. party, Liza wants to leave, Judy prefers to stay.

“You don’t know anybody here.”

“They seem to know me!”

And she can’t sleep. Ever.

Flashbacks take us to young Judy’s (Darci Shaw) “Over the Rainbow” breakthrough, where the “diet pills” and sleep deprivation began at the insistence of history’s worst stage mother (Natasha Powell) and on direct orders — always purred, rarely threatened — of MGM studio chief Louis B. Mayer (Richard Cordery).

“You’re my FAV-orite, Judy,” he says, noting that the “normal life” he hears in her longing for a regular meal, decent hours and the occasional nap is for other girls, all “prettier than you,” but destined for “small lives. Not Judy, She’s got “that VOICE.”

But “that voice” is unmistakable, big and deep and throaty, with the hint of an edge to the enunciations. Much of “Judy” takes place on the stage of London’s Talk of the Town supper showclub, with Zellweger singing the Garland standards — “Come Rain or Come Shine,” “The Trolly Song” and that one about the rainbow.

And Zellweger, an Oscar winner who masters the fidget, the crooked smile, the speaking voice — a posh affectation not-quite-smothering her Minnesota accent — and does her own singing, cannot make us forget Garland’s unique and iconic sound.

There’s no shame in not being able to replicate Judy Garland in song. Who could, other than Liza? But in recreating someone “you won’t forget,” this shortcoming — a hole in a perfectly servicable screen biography — “Judy” makes Garland sound forgettable.

The director of “True Story,” Rupert Goold, tracks us through Garland’s struggles leading up to and through her storied, and yes notorious final London club engagement.

Michael Gambon is the promoter/club owner who books her, Jesse Buckley plays the club factotum meant to be Judy’s “handler” for this version of “My Week With Marilyn.”

Garland is almost unfailingly polite, unless she’s drunk. Her stage fright, at 47, makes her a helpless and hopeless diva, somebody shoved in front of the microphone, shaken, from opening night onward. She’s worthy of our pity.

Perhaps there’s historical accuracy in the techty relationship between Rosalind Wilder (Buckley) and “the world’s greatest entertainer.” There’s nothing warm about it, either.

The younger man/entrepreneur (Finn Wittrock) Judy hooks up with at that L.A. party and later marries is also someone kept at arm’s length by the script. Was he another gay man, who were historically catnip to the Gumm, Garland and Minelli women?

The warmest scene has Judy connecting with two gay fans at the stage door, going to their place for scrambled eggs when there are no London restaurants open after midnight. That’s a play in itself, and if more of the movie had been this intimate, we’d already be stamping Zellweger’s name on the Oscar. It’s warm, musical (singing like Garland this late in her career is easier than it would have been at her “Star is Born” peak).

The flashbacks resonate, with Judy insecure about her looks, her weight, rejected by Mickey Rooney, hectered by her mother, kept in her place by the creep Mayer. And exhausted, always desperate for sleep.

But there’s no power to them.

Although Zellweger handles the few jokes well — a doctor asks, “Take anything for depression?” “Four HUSBANDS!” — there aren’t enough to make this rather somber picture achieve joy. Only in the finale do we have a bittersweet taste of that.

Despite a good cast and a scattering of big names in it, “Judy” feels malnourished, as if Zellweger’s reduced box office status wasn’t able to attract a more flamboyant Mayer, more charismatic players surrounding her.

If we remember Garland, and she is fading even as a gay icon, it will be due to that voice, those films, the glorious bits of camp and “Show must go on” pluck that you can find in scores of Youtube videos of her TV appearances and the occasional concert.

On a musical bio-pic scale, this isn’t “Rocketman” or “Bohemian Rhapsody,” not “Coal Miner’s Daughter,” “What’s Love Got to Do With It,” “Sweet Dreams” or “Get on Up.” It’s unfortunately a lot closer to “Jimi: All is By My Side.” Uncanny in its impersonation, flat as a movie, forgettable as a biography.

MPAA Rating: PG-13 for substance abuse, thematic content, some strong language, and smoking

Cast: Renée Zellweger, Jesse Buckley, Rufus Sewell, Darci Shaw, Finn Wittrock, Michael Gambon

Credits: Directed by Rupert Goold, script by Tom Edge, based on a play by Peter Quilter. An LD Entertainment/BBC Films/Roadside Attractions release.

Running time: 1:58