Few comedians ever play London’s O2 Arena and fewer still manage three nights in a row. Those who do tend to have some things in common: a relatable observational style, limited creative ambition and ruthless commercial savvy. None of which applies to Flight of the Conchords, perhaps the unlikeliest act ever to reach those airless heights of the comic stratosphere.

I saw Flight of the Conchords last week, warming up for their forthcoming arena tour with a run at the 140-seat Soho theatre. Watching their suite of kooky songs about medieval romance, piano-playing seagulls and spoon thieves, laughing at their low-key chat and minutely detailed interplay, the thought of their imminent transfer to arena stages was supremely incongruous. Not least to the Conchords themselves. “We’ll keep that in for the O2,” they’d remark, after this or that improvised quip or ramshackle moment of fun.

If you first saw Bret McKenzie and Jemaine Clement, as I did, in a dingy cellar on the Edinburgh fringe 15 years ago, you may struggle to wrap your head around the scale of their new tour. But if you factor in a Disney film, writing an Oscar-winning song for The Muppets, a sleeper hit HBO sitcom, and the fact that this musical-comedy duo is one of the funniest and most talented acts to come along in two decades – well, an explanation begins to take shape.

It’s certainly not down to any dead-eyed careerism. In my 20 years of interviewing comics, few appeared as shambling and un-starry as McKenzie and Clement in 2003 – the year they were nominated for Edinburgh’s Perrier award. The previous year, theirs had been the festival’s breakout show, due largely to word-of-mouth enthusiasm spread by fellow comics.

Facebook Twitter Pinterest Watch the song Hiphopopotamus vs Rhymenoceros, from episode three of Flight of the Conchords.

Their shtick was artless banter spliced with improbable comic songs, notable for their pernickety lyrics and eclectic musicianship. Zoological rap battle Hiphopopotamus Vs Rhymenoceros was an early favourite (“They call me the Hiphopopotamus / My lyrics are bottomless” and “I’m not a large water-dwelling mammal / Where did you get that preposterous hypothesis?”). The Humans Are Dead, with its “binary solo” and robo-vocal account of the apocalypse, was another, while their Space Oddity spoof Bowie’s in Space was achingly near the mark.

With just a couple of acoustic guitars and a digital glockenspiel, they were maestros of every pop music style imaginable, although they concealed their talent with gags. “You can tell when we’ve learned a new chord,” they told me, “because we’ll use it in our next three songs.” On stage, they played losers who thought they were winners. Off stage, they were winners who pretended to be losers. They’d been invited to Hollywood to pitch a project, they told me – but “you needed a clear idea of what you wanted to do, and we didn’t have any idea at all”. So they were sent packing.

I left that interview unsure whether I’d met the “real” Clement and McKenzie or an extension of the gormless act. From the off, they excelled at scrambling truth and fiction – as per the blissful bit of onstage dialogue in which they guess when the other is in character (“You’re in … now you’re out … now you’re in …”) It helped that they took deadpan to whole new tiers of blankness.

They're so dry and so Kiwi. We're at the bottom of the world, so constant self-deprecation is common in New Zealand Rose Matafeo

“It’s so dry and so Kiwi,” says their compatriot and fellow comic Rose Matafeo, who is not alone in tracing much of the Conchords’ distinctiveness back to their national character. “The constant self-deprecation, the playing it straight, these are so common in New Zealand. We’re at the bottom of the world, so isolated. We’re like what would happen if you left someone alone in a room for a day.”

Jarred Christmas, another New Zealand comic, is surprised how far this took them. “I never thought there’d be an international embrace of that. I’d never seen that happen, comedy-wise.” Christmas co-starred in the Conchords’ eponymous 2005 Radio 2 sitcom, as did Jimmy Carr, Daniel Kitson and Rob Brydon (the Conchords have always surrounded themselves with fast-rising talent). “What struck me,” Christmas says, “is that no matter how laidback they are, they’ve always believed they’re good enough. You’ll notice that, on the radio show, not one of their songs was played in full. So they retained the rights, rather than those defaulting to the BBC. Clearly, they had their sights set on something bigger.”

Facebook Twitter Pinterest No struggle, just placid acceptance … the HBO series Flight of the Conchords. Photograph: BBC/Paul Schiraldi/HBO

Something bigger duly came in 2007, with the launch of the duo’s HBO sitcom, again eponymously titled. They played themselves as hapless immigrants in New York, making zero impression as a band whose manager (played by Rhys Darby) moonlights as a cultural attache at the New Zealand consulate. The series feigned to mock their homeland’s eccentricity and boringness. But, really, it celebrated those qualities. Eccentricity and boringness were the show’s touchstones, while its USP was the radical flatness of McKenzie and Clement’s performances. They took the faux-real stylings of The Office et al and ratcheted up the humdrum, but combined it with wildly incongruous bursts of song in which Bret and Jemaine’s fantasy lives paraded across the screen.

The show ran for two series, featuring soon-to-be-illustrious co-stars (Aziz Ansari, Kristen Wiig) and winning Emmy nominations. Clement and McKenzie also won a 2008 Grammy for best comedy album. The series was never more than a cult hit, in the UK at least, but its significance outstripped its ratings. It opened the world up to indie Kiwi culture and alerted American TV to overseas talent. Where McKenzie and Clement led, the likes of Trevor Noah, John Oliver and James Corden have followed. Likewise, in its depiction of failure, in its disdain for TV conventions (it was part-improvised), and in its uniquely hip brand of musical comedy, the show proved more influential than its modest impact at the time might suggest.

Conventionally, failure in comedy has been something to rail against: it’s the struggle that makes it funny. In Flight of the Conchords, there is no struggle, just placid acceptance. “It showed you didn’t have to be an alpha male,” says Christmas – and in so doing, it flew the flag for a new generation making more arty and intimate, less obvious and aggressive comedy. But it cross-fertilised that strain with the gentle surrealism of Spaced and The Mighty Boosh, to show that you could be dorky losers and rock gods, confirmed bachelors and lotharios.

No matter how laid​​back they are, they always believed they’re good enough. They had their sights set on something big Jarred Christmas

Key to this were the songs, two per episode, that underscore the flights of fancy that offset (or should that be overtake?) Bret and Jemaine’s feckless real lives. The songs alter the reality, moving the plot along in unreal ways, as if singing yourself out of loser-dom really were an option. Narratively, it made tenuous sense, but you were enjoying the songs too much to care.

“One of the hardest things in musical comedy is to write a number that people want to hear again,” says Phil Nichol, of 1990s Canadian musical comedy act Corky and the Juice Pigs. “Usually, once you’ve heard the jokes at the end of each stanza, you know all you need to know. But both Jemaine and Bret are amazing musicians. They write stuff that makes you think, ‘Wow, why didn’t I write that?’ Their songs are exceptionally replayable.” Many of them match or even eclipse the tracks they pastiche – such as the Emmy-nominated Carol Brown (based on Paul Simon’s 50 Ways to Leave Your Lover), or the Peter Sarstedt take-off Rambling Through the Avenues of Time.

Facebook Twitter Pinterest The villainous crustacean Tamatoa voiced by Jemaine Clement in Disney’s Moana. Photograph: Allstar/Walt Disney Productions

It’s certainly a rare feat to make musical comedy cool. A rarer feat still is to graduate from writing funny songs to winning best song Oscars, which McKenzie did in 2012 with Man or Muppet from that year’s Muppets movie. Clement’s interim career has been even more eye-catching, with voiceover roles as Fleshlumpeater in Steven Spielberg’s The BFG, as the villainous crustacean Tamatoa in Disney’s Moana, and as intergalactic criminal Boris “the Animal” in Men in Black III.

“People who discovered them at the movies have then gone back and watched Flight of the Conchords,” says Christmas. “And the sitcom did what The Office did: it stopped at its peak, arguably before its peak, so people have remained perpetually desperate for more.”

And now they’re getting it, as McKenzie and Clement touch down for the UK leg of their world tour. “They’ve just been so consistently good over their entire career,” says Matafeo, who credits the life she’s living today as a New Zealand comic, based in the UK and working internationally, to their example. “Everyone has their own special relationship with a stage of the Conchords’ career. Some people saw them early, at Edinburgh. Some people – like me – remember downloading bootlegs of their songs from the internet. And some people came to them after the sitcom finished. It’s all been so good that, whenever you encounter them, you fall in love with them.”

Flight of the Conchords are at Portsmouth Guildhall from 5-7 March. Then touring the UK until 3 April. Phil Nichol’s tour Your Wrong starts in September.

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