Armando Ianucci’s CV is fit to bursting with side-splitting stuff. If we’d forgotten, we got a reminder when he received a Writers Guild gong at this year’s Comedy Awards, and they played clips of his successes – Alan Partridge, The Day Today… It would not be overstating it to say that, along with Caroline Aherne and Ricky Gervais (arguably!), he has defined British comedy for his generation.

That’s right, British. So it was with no small bit of dread that I learned he and co-creator Simon Blackwell were taking In The Thick of It stateside, building on the Oscar-nominated success of In The Loop, and putting home-grown humour into the White House for Veep – describing the boil and bubble that go into running the smooth-looking machine of the Vice-President’s office.

The good news is that, from the first episode alone, they've done it. Instead of pandering to any American expectations, Iannucci has brought his international audience round to his notions of what’s funny. This proves two things a) that the lines of American-British humour are increasingly blurred as we soak up other’s influences, both in creating and watching, and b) Iannucci is still very, very funny.

The show hits the ground running, with Julia Louis-Dreyfus, Senator Selina Meyer turned Vice-President (hence Veep) walking and talking a la West Wing, beseeching her aides to give her honest appraisal of her new look, before over-riding them, inevitably: “Glasses make me look weak, wheelchair for the eye.” And we were off.

The show rides or falls on the power of Louis-Dreyfus, stalking the corridors of power and relying on and despising her staff in equal measure. She looks fabulous, and flips between bemused, beseeching and belligerent. When she’s in danger of being cornered in a meeting, she instructs her staff, “Get me out of here. Surround me like a human motorcade.”

Confronted with a speech redacted out of existence, just as she walks onto stage to make it, she screeches, “What’s left of this speech? I have hello and prepositions.” It’s early days but all indications are Iannucci has created another comic creation to join the ranks of Partridge and Co.

If Meyer's entourage aren’t quite up to the peerless Thick of It troops, they’re game enough with some dissonance already present in the ranks. “What can’t you do?” Selina asks rapturously of her new favourite, Dan. “Foreplay, direct sunlight…” we hear somewhere from behind.

It’s scarily quick and dense, the holy grail of comedy that you don’t mind watching twice, back to back, to make sure you catch everything. It’s a wonder that Iannucci and his co-writer Simon Blackwell have so much untapped, imaginative venom left in them and it seems that US politics has provided them with another deep well to draw from.

The Veep herself bags many of the best lines for now, but that’s because there’s no equal adversary yet in sight. That’s the only thing this programme needs to move it away from the pack – a tireless campaigner of hostility whose own well of vitriol is buried deep into the earth, with fathomless powers of breadth and self-regeneration. Yes, Mr Tucker, your (other) country needs you…

Veep is playing in the US on HBO. Watch this space for its arrival on these shores.