This sweet, sad film is about a little-known final chapter in the lives of comedy legends Stan Laurel and Oliver Hardy. In 1952, at a low point professionally, out of fashion in the United States, their relationship under stress and needing money, they took on a British tour, sometimes to painfully sparse audiences. Recently we had Film Stars Don’t Die in Liverpool, about Gloria Grahame’s theatrical engagements in Britain. Well, here were film stars dying night after night in Newcastle, Glasgow and Worthing. Jon S Baird’s feature appears fictionally to conflate the tour with the wintry mood of later UK tours when Stan and Ollie’s health and career worries had escalated further. It has a persuasive feel for this twilight of the comedy gods.

Steve Coogan and John C Reilly give great portrayals of Laurel and Hardy. These portraits are detailed, closely observed labours of love, especially as Coogan and Reilly had to nail both the screen personae and also fabricate a subtler, more naturalistic account for the off-stage versions. It is usual for critics to talk about performances going beyond “mere” impersonation, as if impersonation at this level was easy, or had nothing to do with acting. But these are brilliant impersonations, the kind that can only be achieved by exceptionally intelligent actors; the superb technique of both is matched by their obvious love for the originals.

My reservation is that there is something occasionally underpowered and genteel in the film’s gentle nostalgic melancholy. Director Baird and screenwriter Jeff Pope offer interesting insights on the subject of what it is, or was, to be famous. Their film shows the boys in their great 1930s heyday, making movies for the testy Hal Roach, played by Danny Huston. They look like modest, unassuming people doing a professional job. Both then, and in their decline, when they walk among mortals – stagehands, technicians, members of the public – there are no shots of people gasping, gawking, double-taking and trying to siphon off some of their celebrity, as would now be the case in the selfie/social-media era. And Laurel and Hardy went beyond the banal notion of celebrities, maybe even beyond the idea of stars. They were titans. The fact that they are largely unnoticed in boring old Britain’s rainy streets is a sad sign of their decline, and yet in those days, even the most renowned could walk around in public relatively unmolested.

Stan and Ollie accept with a weary lack of diva-ish petulance the measly theatrical digs, the second-division venues, the miserable weather, and the fact that their British producer, Bernard Delfont (Rufus Jones) seems more excited about a new young client called Norman Wisdom. Having been induced to do more strenuous promotional work, for no extra money, box office picks up. But things are not necessarily made any easier by the fact that their wives come out to England to be with them: the protective Lucille Hardy (Shirley Henderson) and the imperious, arrogant ex-dancer from Russia, Ida Laurel (Nina Arianda), both of whom act almost as the id for each man, peevishly voicing the secret resentments bubbling inside the heads of Stan and Ollie, but which they are politely keeping from each other. One outburst from Ida – about Ollie’s one-time disloyalty in doing a movie without Stan – triggers a furious and painful row.

There is a lovely scene in which Stan has to visit Ollie after his larger-than-life partner suffers a mild heart attack. It is a bizarre echo of their famous “hospital visit” sketch which they’ve been doggedly performing on tour – and which is, indeed, very funny. I found myself laughing at it, almost as I would at the original. Both men are intensely aware of the ironic echo, and it makes them reserved, withdrawn. There is a muted charm in that scene, and muted charm in the film generally.