In a scene at the start of In The Loop, the film adaptation of Armando Iannucci's political satire The Thick Of It, a politician and his aide travelling in a ministerial limo take simultaneous calls from satanic spin-doctor Malcom Tucker (Peter Capaldi).

As their smartphones chirrup and the same caller name comes up, they turn to each other and ask: "How does he do that?"

Right now I'm wondering the same thing about Iannucci himself: the Glasgow-born writer seems to be tweeting from the back of a London taxi at the same time as he's talking to me on his phone. Adding to the real-time strangeness of the moment is the fact my computer is also showing tweets from Alastair Campbell, widely viewed as the model for the potty-mouthed Tucker. The former spin-doctor is moaning about having to write his own jokes for the edition of Have I Got News For You? he has just finished recording.

I relay this last bit of information to Iannucci. "Oh dear," he simpers, not sounding the least bit concerned about Campbell's travails. Days later this barely concealed dislike will erupt in a high-profile Twitter spat over the news that Iannucci has accepted an OBE and, to Campbell's mind, joined the Establishment he seeks to lampoon.

Right now, however, the subject at hand is the disorder of the American empire, not an honorific named for the British one. Specifically it's Veep, Iannucci's bold new comedy for HBO which makes its British debut on Sky Atlantic tonight.

Starring Seinfeld mainstay Julia Louis-Dreyfus, Veep follows the fortunes of vice-president Selina Meyer and the team of odious advisers, self-serving aides and cynical spin-doctors which surrounds her. If that sounds terribly familiar, it's because Veep is what Iannucci calls "a cousin" of The Thick Of It.

"We certainly took the theme in terms of the writers and the creative method," he says. "[Otherwise] it's a completely blank sheet. In The Thick Of It, the minister is low level, un-influential, slightly anonymous, always being told what to do whereas in this it's the vice-president. Nobody could speak to them the way Malcolm Tucker speaks to a minister."

This isn't the first time a version of The Thick Of It has been tried in the US. In 2007 a pilot with the same title and set in the US Congress was commissioned by ABC. The channel, as Iannucci notes wryly, is owned by Disney. "It was sold by the BBC to the wrong network," he says. "The moment that happened we knew that what made The Thick Of It what it was just wasn't going to happen."

What he means is that the epic swearing which made TTOI such a sensation wasn't going to happen, nor the withering satire or the barbed, often cynical humour. He's probably right. All three are present and correct in Veep, however.

To date, Iannucci hasn't had any indication of how US politicians view the show itself, though it has just been commissioned for a second series so they'll have plenty of opportunity to watch it. But his entry visa hasn't yet been revoked, he says, so he takes that as a small measure of acceptance. Not that acceptance is a foregone conclusion, even for a comedy writer as acclaimed as Iannucci. "There isn't that tradition of making fun of the presidency. You can make fun of the person but not the office, so it's been interesting being one of the first to do that," he says. "So far it's gone well."

And if it doesn't, there's always Iannucci's just-announced Alan Partridge film to fall back on as well as a new series of TTOI. So how is Malcolm Tucker enjoying life in opposition? Iannucci laughs as the spectre of Alastair Campbell rises up once again. "He finds it very, very frustrating."

Veep is on Sky Atlantic tonight at 10pm.