Before my interview with Armando Iannucci begins, things go wrong. A man from a conferencing service in Melbourne calls to say there’s a technical issue. A publicist from Perth rings, saying they are tracking down the right phone number. Then the great political satirist himself calls directly from his own mobile phone in the UK, apologetic and a little flustered, saying something about delays and the previous interview.

These amusingly tangled communications later strike me as vaguely Iannucci-esque: a situation you might see in one of his productions, which include television’s Veep and The Thick of It, and feature films In the Loop and, now, The Death of Stalin (opening in Australian cinemas 29 March). Although in Iannucci’s hands, a muddle like this would likely include many more profanities, and possibly some despicable character like Malcolm Tucker on the other end of the line.

It doesn’t take long for our conversation to venture into discussion of Australian politics. On the question of how the local machinations are perceived by politics wonks overseas, Iannucci’s response is, perhaps, unsurprising: “We’re aware of the changing prime ministerships every two or three years ... The back-stabbing, the rivalries, the factions and the in-fighting. It is like ancient Rome. As soon as the emperor’s dead, everyone’s now thinking ‘OK, how can I get rid of this emperor so that I can be the emperor?’”

Political power-grabbing is a core theme of The Death of Stalin, which the satirist directed and co-wrote. Based in Moscow in the 50s, the film – loaded with his trademark wit and caustic one-liners – revolves around a group of parasitic politicians who jostle for top spots in the aftermath of the titular dictator’s death.

For a satirist whose scope spans international politics, part of the job entails keeping up with overseas news. Thus Iannucci’s knowledge of recent goings-on down under. “I don’t think there’s been anything hilarious happening in Australia recently with the Coalition,” he deadpans. He adds: “I’m joking, of course. It’s been hilarious with them in the last couple of weeks, hasn’t it?”

Iannucci is referring primarily to the demise of former deputy prime minister Barnaby Joyce, who he met on the Q&A panel last year. Around the time of our interview, the farcical sight emerged of Michaelia Cash, Minister for Jobs and Innovation, using a whiteboard to hide from the media. This again strikes me as rather Iannucci-esque. Do these sorts of incidents surprise him anymore?

“Sadly, they don’t,” he says. “It’s sort of why I stopped doing the shows, because fictional versions of what’s going on at the moment wouldn’t match what’s transpiring in reality. Something has also become magnified, because we’ve reached a kind of media saturation point ... There’s a sort of hysteria about anything that would normally just be quite amusing.”

Something that did surprise Iannucci was when Malcolm Turnbull, during the 2016 federal election campaign, appeared to pilfer a campaign slogan used by Selina Meyer, the fictitious US president in Veep played by Julia Louis-Dreyfus. Meyers’ “continuity with change” became Turnbull’s “continuity and change”. When Iannucci discovered this, he laughed.

“We had tried to come up with something that sounded like a campaign slogan, but when you analyse it, it means nothing. Just two contradictory words,” he says. “It’s like saying ‘sour yet sweet’. What do you mean, sour yet sweet? It’s either one or the other. You can’t have both.

“We know that all the political researchers and advisers watch the show. So you just think, subliminally: are they trying to get it in a speech for a bet? Are they betting with friends that they can get Malcolm Turnbull to say that line? Have Australian dollars changed hands?”

The possibility of an Iannucci-produced satire about Australian politics is a tantalising idea. After all, his approach to comedy has proven to be pliable, successfully applied to politics in Britain (The Thick Of it) as well as America (Veep) and now the former Soviet Union.

“These things are sort of everyman’s stories, in that they are about the workplace and who you socialise with,” he says.

“When I’m doing these political shows, what I’m trying to show is that it’s actually human beings behind this, not machines. It’s just human beings trying to get through the day, and hoping they haven’t cocked up. Every country has its own dynamic, but that’s a universal thing.”

• The Death of Stalin is in Australian cinemas 29 March