Amid the lunchtime burble of London’s Soho House, Mr Mo Gilligan is stretching his arm up to the ceiling, his face a mask of twitchy exasperation. The 31-year-old stand up, social media star and newly minted chat-show host isn’t eager for the bill. No, he is – in the uncanny, meticulously observed style that has become his hallmark – trying to convey just how difficult it was to (secretly) upload his early viral sketches, while also working a day job at the Levi’s store in nearby Covent Garden. “The signal in the stock room was so bad that I’d be going, ‘Come on, come on, come on’ with my arm up,” he says, finally breaking into laughter. “Then we’d close the shop and I’d check the comments [on the video] on the way home. And sometimes, at that time, I’d be getting maybe 10,000 new followers a month.” He grins. “It helped my creativity because I was like, ‘Rah, man, I’ve got this audience of people that like what I’m doing.’”

Since then, that audience has grown rapidly and significantly. In less than three years, the native south Londoner has quit his retail job and managed to parlay his videos – sharply drawn, short clips of Mr Gilligan embodying everyone from 2000s-era pirate radio DJs and tantrum-ing children to awkwardly chummy policemen and a flatcapped Cockney “geezer” forever asking for a “coupla cans” – into a multifaceted, thoroughly modern comedy empire. He has swelled his online following to more than 900,000 people, sold out 22 dates at London’s Leicester Square Theatre (“Those shows were selling out in two minutes. People thought [the fact we didn’t have any left] was fake”), fronted two hit Friday night vehicles for Channel 4 (the raucous, Bafta-nominated The Big Narstie Show, followed last year by his own more polished, US-influenced The Lateish Show) and received approving digital shout-outs from Stormzy and Drake.

It has, in short, been a pretty successful few years for Mr Gilligan. A warp-speed breakthrough that helped seal his gradual transition from dyslexic class clown to all-conquering meme king. And Momentum, his debut Netflix comedy special – a high-wattage whirl of impressions, live band-assisted musical interludes, personal revelations and fine-hewn millennial nostalgia – has the distinct feel of a well-deserved victory lap. A victory lap made available to a potential global audience of more than 151 million subscribers in 190 countries. “To have a special in itself is sick,” he says, as he first sits down – clean-cut and contemplative in a tangerine Stone Island sweatshirt – mere hours after Momentum has gone live. “But this has come at a time where, with things like Top Boy and Stormzy at Glastonbury, it’s almost like we’re giving our UK culture to the world. And we’re doing it our way, without watering it down.”

It’s an astute observation. Mr Gilligan’s comic voice – which he honed for nearly a decade, working the London stand-up circuit and hosting influential live talent showcase The Sunday Show – is notable for its grime-like, unapologetic specificity. His world of Caribbean matriarchs, fast-talking Essex boys and hoodied “roadmen” foregrounds a very particular kind of youthful, largely black experience. But there is a timeless, almost Mr Peter Kay-ish universality to his onstage depiction of, say, the way different family members dance at a wedding. It’s a potent mix.

Plus, when Mr Gilligan’s sell-out 2018 Coupla Cans tour led to his projects at Channel 4, the significance of it, in a genre still dominated by white faces, was not lost on him. “There was massive amounts of pressure because I was representing the black community,” he says, setting down a ham and cheese toastie. “But there was also the thing of, ‘Don’t make us look stupid. Don’t go on there doing stuff that makes us cringe.’” He does note, however, that the internet narrative around his move from a co-anchor role on Big Narstie’s show, to hosting his own vehicle, revealed a degree of ingrained prejudice. “People were saying, ‘So did you snake Narstie? Does that mean The Big Narstie Show is finished?’” He shakes his head. “It’s not like I’m some chosen one and there isn’t any room for any other [black hosts] after me. The response to a lack of black people on TV shouldn’t be, ‘Oh, well, we’ve got Mo on at 10.00pm, so that’s all we need.’”

The Lateish Show has not yet been commissioned for a second series, but Mr Gilligan seems authentically calm about it (“Not knowing yet keeps me hungry and stops me feeling too comfortable”) and he is similarly level-headed about the flood of other offers coming to him. Film projects? Possibly. A book? Not yet. “My story is just starting,” he says, by way of explanation. One thing he will always do, however – no matter how busy his schedule gets – is film the shareable videos that made all this possible.

“People go, ‘You don’t need to do them now because you got what you wanted,’” he says. “But I just love them. Genuinely.” He flashes that familiar, childish grin. “There’s nothing funnier than having an idea and just bringing it out straight away.” Never forget where you came from, they say. And in many ways Mr Gilligan is still that guy in the stock room, arm aloft, trying to make something happen.

Mo Gilligan: Momentum is out now (Netflix)