Scottish filmmaker Jon S. Baird's Stan & Ollie opens with a bravura tracking shot as world famous double act Stan Laurel (Steve Coogan) and Oliver Hardy (John C. Reilly) walk through a bustling film studio. Gossiping and arguing with studio boss Hal Roach (Danny Huston), they finally arrive on set to perform a scene from 1937's Way Out West – a cowboy-themed story that would, in time, become regarded as their masterpiece.

Aside from being a technically impressive moment, it's a beautiful way encapsulate this comic duo at the height of their fame. But Baird's film, written by Jeff Pope (Oscar-nominated for scripting Philomena), is not about two men conquering Hollywood. The story soon winds on 16 years; Laurel and Hardy are still together but no longer so in demand. Back in postwar Britain, they are on a live tour, in the hope of bankrolling their next picture. But has their time passed?

After football hooligan tale Cass and Irvine Welsh adaptation Filth, this is undeniably Baird's most ambitious film – a classy look at the gruelling nature of showbiz, and issues of loyalty and trust that come with being a double act. The film particularly livens up when Hardy's wife Lucille (Shirley Henderson) and Laurel's partner Ida (Nina Arianda) arrive for morale support. Old wounds are inevitably opened; notably, Hardy's decision to briefly go solo.

Coogan is particularly good at Laurel, totally nailing his on-screen comic persona (one moment, where he tries to entertain a receptionist with a bowler hat trick is done to a tee). Reilly manages to inhabit Hardy too, although the heavy prosthetics do leave him hampered at times. But with Baird and Pope subtly weaving Laurel and Hardy's routines into the very fabric of the story, it's a very loving, affectionate nod to two of cinema's greats.

Screened on Sun 21 Oct as part of the BFI London Film Festival. General release from Fri 11 Jan.