In 1953, Stan Laurel and Oliver Hardy were no longer the box-office giants they had been, but they weren’t yet the legends they’d become. Almost as hapless as the half-witted bumblers they played in their classic films, they couldn’t find work in the US, and so they set off on a tour of British theatres – half-empty British theatres, at that. Hardy had heart problems and a bad knee, which made it painful for him to get through their routines. Their fans’ praise could be pretty painful, too. “I think it’s amazing that you two are still going strong,” chirps one woman in Stan & Ollie, a comedy drama about the 1953 tour, “still using the same old material!”

-       Film review: Robert Pattinson stars in High Life

-       Film review: Two stars for Venom

-       Film review: Colette

The film could easily have been depressing – a tragedy, even, in which a pair of 60-something has-beens face that final curtain. But the film-makers are too deeply in love with Laurel and Hardy to take them anywhere so dark. Directed by Jon S Baird (Filth) and written by Jeff Pope (Philomena), Stan & Ollie glows with respect and affection for its title characters, their long and loyal friendship and their immortal comic brilliance. 

Stan & Ollie is a film you watch with a lump in your throat, but with a smile on your face

It’s also suffused with that nostalgia for mid-20th-Century Britain that is currently keeping the UK’s film industry afloat (see also: Breathe, Their Finest, The Guernsey Literary and Potato Peel Pie Society, and many more). Everywhere, there are spotless steam trains, shiny vintage cars and well-cut suits. Even the supposedly shabby hotels where Laurel and Hardy stay at the start of the tour seem warm and cosy. In some scenes, their surroundings are no more believable than the back projection we see them using when they’re shooting Way Out West. But there is nothing fake about the fondness that Baird and his team have for their beleaguered, disappointed yet touchingly positive heroes. The mood is determinedly upbeat and the dialogue crackles with humour, even when the duo is in another fine mess, as the catchphrase goes. Stan & Ollie is a film you watch with a lump in your throat, but with a smile on your face.

Nowhere is its fondness for Laurel and Hardy more apparent than in the committed performances of its stars, Steve Coogan and John C Reilly. Coogan, of course, plays Laurel (who was from Lancashire in the north of England, as Coogan is). He may have been a whimpering man-child on film, but behind the scenes Laurel is the brains of the operation. A businessman and a workaholic, he resents Hardy’s failure to support him in his contract negotiations with their former boss Hal Roach (a cameo by Danny Huston), but he would rather resort to a joke or a pratfall than talk about his feelings. When Laurel and Hardy aren’t on stage together, he is alone in his room, polishing the script for the Robin Hood comedy he is planning.

Hardy, played by Reilly, goes along for the ride. Ollie was the one with the grand plans on screen, but off screen he is content with a drink, a cigarette and enough money to pay off his bookmakers and ex-wives: his two biggest vices are horses and divorces.

Coogan and Reilly do an extremely difficult job extremely well, in that their versions of Laurel and Hardy are recognisable as the iconic clowns from the duo’s own films, but also convincing as rounded human beings. Reilly has Hardy’s dainty finger-waggling wave and his bashful smile, and Coogan has Laurel’s adenoidal mewl and his fussily precise mannerisms. And having been Alan Partridge for so many years, he is a past master at playing a celebrity who can present a professional mask to the cameras, cracked as it is by insecurities.

The actors are so skilled, in fact, that you soon stop noticing the rubbery prosthetics. Reilly’s false jowls make him look as if he has a balloon wedged under his chin, while Coogan’s artificially elongated jaw gives him a strange resemblance to Rob Brydon, his own comedy partner in Michael Winterbottom’s The Trip. But the men are so comfortable in their roles, and with each other, that by the end of the opening scene – a slick six-minute tracking shot of “the boys” walking and talking through a Hollywood studio in 1937 – you’ll be willing to accept that them as close friends and colleagues, and you’ll relish the prospect of being in their company for the next hour and a half.

Not that Coogan and Reilly turn in the film’s only awards-worthy performances. Nina Arianda and Shirley Henderson come close to stealing the show as Laurel’s wife Ida and Hardy’s wife Lucille, respectively, who join their husbands in England for the tour’s last dates. If Laurel and Hardy are fundamentally too nice to one another to supply the conflict that this sort of true-life drama demands, Mrs Laurel and Mrs Hardy make up the shortfall, and the sniping between the tough Russian and the sharp American provides some of the film’s funniest sequences. “Two double acts for the price of one,” cracks the tour’s slippery British promoter (Rufus Jones, who comes quite close to stealing the show, too) – and he’s right.

When the time comes for the lead characters to vent their frustrations in an inevitable argument, it’s a short, forced exchange which suggests that nobody’s heart is really in it. While most biopics of showbiz double acts revel in the participants’ mutual loathing, Stan and Ollie prefers to get past the disagreements as quickly as possible, so that its heroes can get back to crooning The Blue Ridge Mountains of Virginia from Way Out West, or recreating the hospital visit from County Hospital.  

Nothing much is at stake. It’s not exactly a spoiler to say that Laurel and Hardy didn’t become Hollywood superstars again in the 1950s, so you know all along where the tour is heading: there is less tension in this film than there is in most of the duo’s comedies. But Stan & Ollie is a homage – a tip of the bowler hat – that is too heartfelt to resist. It’s not another fine mess, but a fine bromance.

★★★★☆

If you would like to comment on this story or anything else you have seen on BBC Culture, head over to our Facebook page or message us on Twitter.

And if you liked this story, sign up for the weekly bbc.com features newsletter, called “If You Only Read 6 Things This Week”. A handpicked selection of stories from BBC Future, Culture, Capital and Travel, delivered to your inbox every Friday.