For Judy Garland fans, the final station of the cross in the ordeal of her last years was a five-week booking at the Talk of the Town nightclub in London in 1969, which she desperately needed for the money. In those famous and often chaotic concerts she appeared frail, unwell, tipsy or bleary-eyed: mannerisms that she had long since semi-consciously incorporated into her live act. But they were real at some level. Also real were the many flashes of the old magic; emotional arias made more glorious for having been wrenched from her battered heart. This movie is about that troubled period: a defiant last stand in full view of her passionately supportive fans. It was Judy’s emotional Alamo in the face of parasitic husbands, spiteful press and misogynist showbiz overlords – beginning with studio chief Louis B Mayer, who ruined her childhood on the yellow brick road to stardom.

Judy is adapted by screenwriter Tom Edge from Peter Quilter’s stage play End of the Rainbow, and is directed by Rupert Goold; Renée Zellweger gives us a heartfelt, studied portrayal of Garland. Her performance and the film itself are forthright and un-camp, though careful to acknowledge the importance of Garland’s gay fanbase by adroitly creating two fictional gay superfans. It is clearly influenced by Garland’s own self-mythologising movie about her British period, I Could Go on Singing (1963), about the gutsy yet vulnerable singing star doing shows at the London Palladium.

But this is really a standard-issue biopic heartwarmer about a Hollywood star in decline and in Blighty: a bit like the recent Stan & Ollie, about Laurel and Hardy’s final British tours. We get the usual sobering biographical grace notes over the final credits, although not the traditional black-and-white photos of the real-life people, perhaps because Judy Garland is just too well known. The film sugarcoats Garland’s physical deterioration, her addictions, her wretchedness and her mortality. However, paradoxically, it’s the most relaxed and personal performance we have seen from Zellweger in a while.

She plays a resilient Judy who has taken all that life has to throw at her and (to borrow a line used in the recent Elton John film Rocketman) she is still … well, sometimes she’s not standing, sometimes she’s actually falling over on stage. But she’s still battling on many fronts, mostly financial, living in California, divorced from her third husband, Sid Luft (Rufus Sewell), and in an acrimonious dispute with him about the children. There’s no money coming in and when the London residency is mooted, she jumps at the chance of solid earnings and a restorative blast of adoration from British admirers. But there’s no chance of taking the children with her, and so she manages loneliness with booze and pills (the film doesn’t do justice to the scale of her drug dependency). She is uneasy with her Brit promoter Bernard Delfont (Michael Gambon), but has support from exasperated assistant Rosalyn Wilder (Jessie Buckley). So the London gigs commence, interspersed with flashbacks to her unhappy childhood on the Oz set, with Darci Shaw as the young Judy. In the present day, there’s a new chance of romance with a handsome cocktail waiter called Mickey Deans (Finn Wittrock). You don’t have to be a Garlandologist to figure out if that is going to end well.

Zellweger rises resolutely to the challenge of playing Judy on stage and off: her eyes crinkle in tandem with a tremulous pout when her feelings are hurt, and sometimes when they are the opposite of hurt, although she is perhaps less convincing with the wide-eyed Garland gaze. Her walk and stance cleverly convey the sense of someone who is only in her 40s but feels older, but is rejuvenated by the electric thrill of being on stage. Yet the movie missed a trick in the way it depicted the difficult relationship with her daughter Liza Minnelli (played here by Gemma-Leah Devereux): there is one low-key meeting between them at a party in which Judy undermines Liza’s confidence, but it is underpowered. Liza herself deserves almost as much mythologising and turbocharged drama as Judy, and a mother-daughter encounter between these icons should really be a showstopper.

There was only ever really one way and one tune to end this film, and it duly arrives along with an interesting and realistic touch about the necessity of not expecting miracles. Zellweger gives us a tribute to Judy Garland’s flair and to that ethos of the show needing to go on being both a burden and driving force. Yet Garland’s terrible sadness is mostly invisible.