The Rubberbandits, I've been warned, only do interviews dressed in character. This partly explains why I find myself in a 15th-century Irish castle, in the company of two men wearing plastic bags on their heads. The characters – Blindboy Boatclub and Mr Chrome – may be fictitious, but their success is real enough. These pranksters turned chart-topping stars have taken Ireland by storm with their swaggering hip-hop comedy skits, weekly sketches on TV, and hugely popular online videos. Having notched up 25m YouTube views in total, they recently put together a pilot for Channel 4, which aired late last year, and are currently in the middle of their debut London run.

Faces concealed behind ripped polythene, the duo trade on drugged-up, feral underclass stereotypes. So when they take me on a tour of the castle's banqueting hall while discussing the French painter Jacques-Louis David, it comes as a bit of a surprise. "But that's our game," says Blindboy Boatclub (AKA Dave Chambers). "You put something smart beside something stupid and see how it works."

We're at Bunratty Castle in County Clare, not far from Limerick, the city the Rubberbandits are indelibly associated with. It was in Limerick that Chambers and schoolfriend Bob McGlynn first circulated CDs of prank phonecalls to local teachers and businesspeople; the place still provides them with material. "It all comes from what we grew up with at school," says Chambers. "Stories we heard, lads we hung around with." The fact that you can see teenagers riding horses through the town's streets, for example, inspired their song Horse Outside, in which a man sees off his romantic rivals by flaunting his steed ("Fuck your Honda Civic/ I've a horse outside"). The track went viral, almost beat X-Factor winner Matt Cardle to the Christmas No 1 in Ireland, and turned Blindboy Boatclub and Mr Chrome into household names.

Although Horse Outside won them mass appeal, it also brought plenty of unwelcome attention. "Ireland was signing an austerity treaty with Germany at the time and everyone called us 'the voice of the poor'," says McGlynn. "The amount of stuff people thought that song was about! It was a song about a horse."

The Rubberbandits are not much given to self-analysis – or at least, not while in character. When I encountered them at last year's Edinburgh fringe, it seemed obvious that their polythene-swaddled faces were intended to be provocative: shorthand for delinquency tending towards terrorism, particularly with memories of England's summer riots still fresh. But, says McGlynn of his headwear, "it's just a bag". They adopted the look for their first live gig in 2007; by then, they'd been anonymous for seven years and wanted to keep it that way. "People didn't know what we looked like," says Chambers, "didn't know where to buy our CD. Drug dealers were selling it with hash in some neighbourhoods – that's how underground we were."

Their act came about partly in response to Limerick's reputation as a poverty-stricken place (it's where Frank McCourt's misery memoir Angela's Ashes is set), riven with gangs, drugs and crime (it's also Ireland's murder capital). "The media portray Limerick as like Compton in LA," says Chambers. "We're taking the piss out of that." Their show is, however, light years more nuanced than, say, Al Murray's Pub Landlord: Chambers and McGlynn are forever subverting any sense of who the Rubberbandits are and what they represent. Take their ode to man-boy love, Spoiling Ivan, which pointedly isn't the cheap paedophile gag you think it's going to be; it's actually rather sweet. Another is Up Da RA, a seemingly pro-IRA football chant that spoofs armchair republicanism.

"Up Da RA is pure satire," says Chambers. McGlynn adds: "But getting Danny Dyer in a headlock – there's no satire there." This is a reference to their video for a less sophisticated number, Liar Liar Danny Dyer, featuring a Spitting Image-style caricature of the actor. "Sometimes," says McGlynn, "we're just acting the bollocks" (ie, taking the piss.) In their weakest material, the line between send-up and celebration of loutishness becomes vanishingly thin – as McGlynn seems to acknowledge when he calls some of their early work "disgusting songs I now regret".

Despite all the humour, the pair are (terrific) musicians first and comedians second: they offer, says Chambers, "songs people can dance to and laugh at at the same time – with punchlines that stick in your head because there's a hook to them". Unsurprisingly, there's no shortage of clowning in their live shtick: at one gig, says Chambers, "we had a giant lump of hash running around and someone dressed as a Garda chasing it."

Having been burned by their brush with mass appeal in Ireland, the Rubberbandits are eager to start afresh in a bigger country. In Britain, says McGlynn, "We can survive on just a hipster audience for a lot longer." The Channel 4 pilot, the station's first Irish production since Father Ted, will grow their UK following, as will their success in Edinburgh; having expected to play to empty houses, they sold well and bagged a Malcolm Hardee award for most original comedy. But bigger audiences might not be their only reason for crossing the water: in Ireland, God help them, they had started being compared to Jedward.