The last time Sam Taylor-Johnson directed a movie about drugs it was A Million Little Pieces in 2019, based on James Frey’s notoriously inauthentic memoir of addiction – and the last time she made a film about a music legend it was Nowhere Boy in 2009, about John Lennon.

Now she brings the two together in what’s easily her best work so far: an urgent, warm, heartfelt dramatisation, scripted by Matt Greenhalgh, of the life of Amy Winehouse, the brilliant London soul singer who died of alcohol poisoning at 27 in 2011. It’s a movie with the simplicity, even the naivety, of a fan-tribute. But there’s a thoroughly engaging and sweet-natured performance from Marisa Abela as Amy – though arguably taking the rougher edges off. The only time Abela is less than persuasive is when she has to get into a fight on the north London streets of Camden.

And Jack O’Connell is a coolly charismatic and muscular presence as her no-good husband and addiction-enabler Blake Fielder-Civil. O’Connell can’t help being a smart, capable screen presence and makes Blake a lot more sympathetic and less rodenty than he appeared in real life – and yet part of the (reasonable) point of the film is that he was a human being, afraid that Amy would leave him for another celebrity, and that media images are misleading.

There’s a lovely, if faintly sucrose scene in which the already boozed-up Blake first meets Amy in The Good Mixer pub in Camden Town (already famous for its association with 90s cool Britannia and Blur) – buzzing with his horse-racing winnings and airily unfazed when the already entranced Amy challenges him to a game of pool while he cheekily lets her (and us) assume he doesn’t know who she is. But of course he does and even one-ups her in musical knowledge in compelling her to admit that she has never heard, or heard of the Shangri-Las’ Leader of the Pack, which he puts on the jukebox and extravagantly mimes to. There is a growing sadness in the realisation that this ecstatic first meeting is the first and last time they will ever be truly happy together.

Perhaps any movie about Winehouse is going to suffer in comparison with Asif Kapadia’s compelling archive-mosaic documentary Amy from 2015, which delivered the woman herself and also gave a clearer idea of her demanding musicianship and professionalism, far from the tabloid caricature of nonstop drugginesss. But this film tries to intuit the part that romance played in Amy Winehouse’s life and the narrative of unhappiness that it created in her work: a poisonous wellspring of inspiration.

And Taylor-Johnson’s film is also much more sympathetic to Winehouse’s father Mitch, the cab driver estranged from Amy’s mother who came back into her life to help manage her career and famously counselled against her going to rehab.

Mitch comes across better here because he’s played with bullish charm and schmaltz by Eddie Marsan – very funny in the scene where he infuriates Amy by coming to an important meeting and siding with the record business execs against her. I actually wonder if an equally good film called Mitch could be made simply about that lonely, complex figure.

Back to Black is essentially a gentle, forgiving film and there are other, tougher, bleaker ways to put Winehouse’s life on screen – but Abela conveys her tenderness, and perhaps most poignantly of all her youth, so tellingly at odds with that tough image and eerily mature voice.

• Back to Black is out in UK cinemas on 12 April and in the US on 17 May