Most fans of Malcolm Tucker's sweary outbursts will know that Iannucci had first thought up the show after arguing on telly back in 2004 that Yes Minister was the 'Best British Sitcom'. Yes Minister stalled at sixth in the BBC's poll, but deserved to rank much higher.
Ahead of its controversial revamp and return later this month on UKTV's Gold, we've dusted off our DVD collections of the series - and its Yes, Prime Minister follow-up - to remind ourselves just how good it was. We've not been disappointed.
Yes Minister. February 25, 1980 - December 23, 1982.
Christmas Special Party Games. December 17, 1984
Yes, Prime Minister. January 9, 1986 - January 28, 1988
Much has been said in the years since its broadcast about the satirical elements of Yes Minister and its follow-up. People talk of how it was watched by those in Westminster - even Maggie Thatcher was a fan.
There are heated arguments about whether the show opened the eyes of the public to the nefarious goings on in the seats of power, or just excused and entrenched a cynicism in the political system that continues to this day. But what really shines through after repeated viewings is what a perfect, character-driven sitcom it was.
The central trio of minister James Hacker (Paul Eddington), his principal private secretary Bernard Woolley (Derek Fowlds) and of course, permanent secretary Sir Humphrey Appleby (Nigel Hawthorne) each get their turn in teasing out full-on belly laughs, sympathy, derision and at times heart-wrenching pathos. And if all else failed, the writers could always give Jim a drink.
Hacker was the newbie minister in the bureaucracy-concerned Department for Administrative Affairs, Sir Humphrey the civil servant whose primary role was to maintain the status quo and foil his minister's every move.
Bernard's role was more ambiguous... sometimes with his political master, but obviously ruled by his more immediate boss. Always bubbling under the skin, almost unnoticeably, was the careerist machinations of a civil service high-flyer. These were all proper, rounded characters.
And they grew. So many sitcoms press the character-reset button at the end of each episode. The very best chart the shifting natures of their heroes and villains as the events we watch each week take their toll.
This was seen in the end-of-series special 'Party Games' which saw Hacker finally realise his Churchillian ambitions and take on the premiership, helped by Sir Humphrey, before he invites Bernard along for the Yes, Prime Minister ride.
Back to the politics, when watching the show in 2013 the most obvious thought is plus ça change, plus c'est la même chose. 'Open Government', 'Doing the Honours', 'The Greasy Pole', 'Big Brother', 'Equal Opportunities' and 'The Compassionate Society' - these are episode titles that could have been written last week.
Despite our modern coalition, the underlying politics seem not to have changed a jot. The main political lesson seems to be that, whoever you vote for, well, the government wins.
What we've not properly mentioned is just how laugh-out-loud funny the show was. Antony Jay and Jonathan Lynn's scripts are often praised for how smart they were, but laughs were never sacrificed on the altar of being clever-clever.
Be it how neatly Sir Humph could talk in circles, Bernard's hatred of a mixed metaphor, Hacker and Humphrey's superfast exchanges or the simple joy of the minister's expressive face moving from expectation or delight to utter horror, not a minute went by without something properly funny happening.
The laughs weren't cheap, either. The secret wasn't that the scripts were "clever". It was that the writers didn't think the audience was stupid. Too many shows treat the people who watch them like idiots - and that contempt shines through the work. Yes Minister was the complete opposite.
Most of the laughs came from the situations and interplay between the three main characters and brilliant guest stars. Perhaps not as three-dimensional as the big three, returning characters like Hacker's put-upon wife Annie (Diana Hoddinott), political adviser Frank "weasel" Weisel (Neil Fitzwiliam), spad Dorothy Wainwright (Deborah Norton) and of course, Sir Arnold Robinson (John Nettleton) all did their bit to add layers on to the show.
But that didn't mean that Yes, MInister wasn't littered with brilliant, quoteable one-liners - most of which came from Sir Humphrey. "Politicians must be allowed to panic. They need activity. It is their substitute for achievement." "The Foreign Office are not spineless. It takes a great deal of strength to do nothing all the time." "The first rule of politics: never believe anything until it's been officially denied."
As Iannucci said in his own argument for the show: "Yes Minister made the driest subject possible - the minutiae of politics - into sparkling comedy... It remains the most quintessentially British of the British sitcoms - understatement, embarrassment, Masonic secrecy and respect for the rules all in evidence."
Yes, Prime Minister didn't quite match the heights of its predecessor - it was a little bit harder to buy into Hacker's impotence with ostensibly the highest job in the land - but it was still consistently brilliant.
Beyond the original show there was a series of books, billed as Hacker's diaries with added bonuses like letters, papers released under the 30 year rule and footnote quotes from an older, wiser Bernard. These were no quick Christmas cash-in, but every bit as witty and funny as the episodes on which they were based.
There was a Radio 4 revival, and, more recently a stage play penned by Jay and Lynn that has inspired this small-screen return. Setting the revamp in the present day but choosing to bring back the characters of Hacker, Humphrey and Bernard has proved controversial.
Will the new Yes, Prime Minister reach the heights of the original? We're keeping an open mind for now. But even if it's a complete flop, we'll always have these 38 episodes of comedic perfection to treasure.
Were you a fan of Jim Hacker? Are you looking forward to his return this month on Gold? Let us know your thoughts in the comments box below!