With political backstabbing continuing apace on both sides of the pond and Russia overreaching, that great British satirist Armando Iannucci helps us to laugh rather than cry as he sends up an even sorrier state of affairs with typical precision. He winds the clock back to Moscow, 1953 and the reign of the eponymous dictator, reimagining the hysteria surrounding Stalin's death as the blackest of comedies and the most exuberant of farces.

Based on Fabien Nury and Thierry Robin's graphic novels, the material is a great fit for the creator of Veep and The Thick of It; yet the comedy here is even wilder in a grotesquely irreverent Marx Brothers kind of way – it's fittingly cinematic, as its players balloon into figures much larger than life. Steve Buscemi, Jeffrey Tambor, Michael Palin and Simon Russell Beale are four bickering members of Stalin's committee, Jason Isaacs is a gruff field marshall, Rupert Friend and Andrea Riseborough Stalin's adult children.

The decision to stick with British and American accents only adds to the hilarity (Adrian McLoughlin plays Stalin like a Cockney Joe Pesci, Isaacs goes full Yorkshire, Buscemi retains his famous New York drawl). Meanwhile, the film has fun with the impossibility of staying in favour in a volatile, insanely unreasonable regime (a wife is thrown under the bus and then awkwardly re-embraced, notes are taken on which jokes have gone down well). It pooh-poohs the idea that even a scrap of decency could exist in such a poisonous environment (when Tambor's Malenkov assumes control his feeble attempts to stem the bloodshed fall flat) and mines considerable comedy from the frantic, predominantly hapless manoeuvring that follows the leader's demise.

The deft interplay of this esteemed ensemble is a consistent joy and it's especially gratifying to find a juicy role for stage legend and perennial screen supporting star Beale as the skin-crawling, brazenly self-serving Beria, whose treatment of women leaves a particularly unpleasant taste – an example of how the film weaves in serious points and solemn moments without losing its humorous edge. And there's ample comic opportunity for those better known for their dramatic chops (Isaacs, Friend, Riseborough).

'Stalin would be loving this,' remarks Palin wistfully, as events reach their bloody climax. Audiences, too, are in for a real treat, with a film as riotously funny as it is alarmingly pertinent.

General release from Fri 20 Oct.