Anthony Horowitz is best known for his teen spy series Alex Rider and newly imagined stories of Sherlock Holmes and James Bond. Now he's come up with the most brilliant idea for a new Ray Cooney farce: Saddam Hussein drops in for dinner unexpectedly when there's plenty you don't want him to know about, starting with a body in the cellar, a turd in the toilet, contaminated water and a dissenter in the ranks.

Hussein used to do this, apparently: turn up for tiffin to both dodge his enemies and meet the people. And this night in particular happens to be the night of the 2003 invasion in search of the weapons of mass destruction. As his flustered host explains to a disbelieving daughter: there are no such weapons; Saddam used them all up in the wars with Iran and Kuwait.

Lindsay Posner's production, on a classic divided domestic interior designed by Tim Shortall, sets it all up perfectly: Sanjeev Bhaskar's Alawi, a builder supervising an extension to the biggest mosque in Baghdad, has been stashing away tiles on the side while insisting his daughter Rana (Rebecca Grant) marries her own traffic cop cousin Jammal (Nathan Amzi) to fulfil her destiny, Jammal says, of bearing his children and cleaning his house.

Rana, of course, loves another, the slightly famous actor Sayid (Ilan Goodman) who has gained entry disguised as a plumber trying to unblock the toilet. Sayid is Sunni, the family Shiah, another cause of friction in the family. And when Saddam's security chief announces the president's imminent arrival, more panic: mother (Shobu Kapoor) has no food ready. Luckily (or unluckily) Jammal has arrived with a bag of brown dates of ambiguous appearance…

Enter Steven Berkoff's amazing Saddam – looking like a cross between Fu Manchu and an embalmed Robert de Niro – and Horowitz and Posner take a series of risks. They slow down the play – Cooney famously makes the situation change with almost every line – to allow Berkoff his own pace and rhythm, as well as a series of self-justifying speeches about the source of his weapons and chemicals in the West and his contempt for the Anglo/American ideological campaign: "We don't want their democracy. Nobody does."

Saddam was always right about that, but Berkoff varnishes his characterisation with such a sleaze-ball sloth and terrifying glazed-eyed demeanour that you know he's right to feel insecure. The risks just about pay off, but a bit of tightening here and there wouldn't go amiss. One of Saddam's guards is peremptorily despatched for yawning but another (identical) one pops up immediately, just as the plumber bears a fortuitous resemblance to the security chief. Nobody's safe, everyone's replaceable, a founding principle in farce as well as in tyranny.

Other well detonated mix-ups involve rat poison and hot spices, an incendiary revolutionary pamphlet, a too-small substitute suit – Bhaskar trying to get things cooking in an awkwardly restricting hose and jacket revives glorious memories of Derek Royle in classic Cooney – and a glass of water that results in the most sustained and hilarious fit of farting eructation I've ever seen on a stage. Smells like a hit.

Dinner with Saddam runs at the Menier Chocolate Factory until 14 November 2015.