When Dublin native Alex Anyaegbunam aka Rejjie Snow first told people he wanted to be a rapper, he would often get the same response: “But you’re Irish?’”

“Nearly everyone said that,” he says with a laugh. “It kind of sucked. But I always knew what I wanted to do. I used it as fuel to prove everyone wrong.”

The naysayers had a point: Ireland is not exactly known as a hotbed of contemporary urban sound. Yet Snow can now justifiably claim to have to have planted his country’s flag on the hip-hop map.

Still just 24, his star continues to rise. As far back as 2011 he was uploading tracks online under the alias Lecs Luther; when he landed in London in 2013, he fell in with a crowd south of the river that included King Krule (whose couch he slept on while he found his feet) and Loyle Carner. Carner sang on Snow’s self-released debut EP, Rejovich, which reached the top of iTunes’ hip-hop chart, dethroning Kanye West’s Yeezus.

The video for his track “All Around The World”, featuring Lily-Rose Depp, racked up half a million YouTube streams in its first week, leading Madonna to personally request Snow be her support act on the Rebel Heart Tour. “I was like ‘is this for real?’ Does she know I’ve only got seven songs?’” he recalls.

Mouth almighty: Snow released his eclectic debut album 'Dear Annie' last year

By 2016 he was playing shows with Kendrick Lamar and became the first non-US artist signed to 300 Entertainment, home to rap prodigies Young Thug and Fetty Wap. Such was the expectation for his debut album Dear Annie – 2017 mixtape “The Moon and You” proved a curious stopgap – he sold out London’s 3,300 capacity Roundhouse before it had even been released.

Understandably, it can seem a bit much. “Imagine that moment when your chair tips just a little too far back. That's how I feel all the time” he tweeted recently, and he admits to being overwhelmed.

“I’ve felt the anticipation from everyone, from fans to family and friends. Behind closed doors it’s been panic. It’s a relief now the album is out.”

We are sat upstairs at lunchtime, drinking tea in a private members club in central London. Snow is gearing up for his second leg of UK dates this year. He’s feeling the effects of touring – “it’s bad for my health” – but you wouldn’t guess: among the business types and hipsters talking shop, Snow is incongruously street-stylish in colourful tracksuit and Barcelona football shirt.

He’s exceptionally easy-going and quietly charming, but underneath a slacker façade lies a serious self-critic who doesn’t suffer fools. “Sometimes I feel like I don’t deserve certain things, and think why am I doing this? I have trust issues with people in the music industry, it’s full of weird people. I can’t let certain things slide. I don’t forget shit.”

He speaks in short sentences in a laconic drawl of an accent that has had its harsher Irish edges sanded off by a nomadic few years. At 17 he moved to Orlando, Florida on a football scholarship, which he soon decided wasn’t for him. “It tailored around athletes so it was intense, football every day. But I didn’t have the dedication”.

He quit American education a second time, from an arts course in Georgia, to move to London to make a go of music. “Leaving school to do it was a big deal. I had to make it work. There was no other option.”

Rejjie Snow performs at Olympia Theatre in Dublin (Getty)

He’s since spent extended time in New York and Paris, and says wherever he goes, people are surprised he doesn’t conform to stereotype: “I’m not what people expect, and that’s funny because I’m just being myself. Of course I understand the stereotypes that hip-hop is associated with, but that’s not me. If it’s not you, you shouldn’t try and play the game.”

To peg Snow as merely hip-hop is wrong in any case. Dear Annie has been so long in gestation precisely because Snow’s vision has been shifting from his Tyler, The Creator influenced early work into a genre-fluid expression of his musical DNA.

“I don’t actually listen to much hip-hop,” he says. “I love Michael Jackson and Queen and pop and R&B. I think I’ve moved away from just being a rapper. On a creative and artistic level I’m way more myself now. I don’t make music like anyone else for the most part.”

Featuring collaborations with Kaytranada, Anna of the North and Jesse James Solomon and produced by Rahki (Kendrick Lamar), Dear Annie is a superb, 20-track, hour-long odyssey that takes in spacey jazz, soul jams, West Coast beats and Eighties funk, and sees Snow rap – and croon – about love, sex, loss and depression with bold clarity.

Committing his feelings to tape was a freeing process. “I’ve matured a lot. I wasn’t ready to do that at first. I’m not really an open person, it was hard to share and be open about my feelings. Until I met my partner I never felt comfortable talking about that in the music. It’s what made the album become what it is.”

It can be dark: Snow recently lost friends – “it is what it is, you just have to make the most of people when they’re around” – but it’s also full of levity. Anna of the North duet “Charlie Brown” is laugh out loud funny; during one spoken interlude, he jokes he’s “Irish, but not from the waist down”. He laughs when I mention it. “I had to put that in there to let people know about it, it’s all good.”

The skits on the album are the only time his Irishness is apparent – his lexicon and flow are more American. “For me it’s not that important to my music. If you come from Dublin you’d know I was from there with my humour, certain things I do. But in terms of other people I don’t expect them to understand.”

Out on his own: 'I don’t make music like anyone else'

Snow’s mother is adopted Irish-Jamaican, his father Nigerian; his grandfather was a Nigerian judge who aided Afrobeat legend Fela Kuti when he was in jail. Growing up Catholic (“my granny would make me go to church, I hated it”) and black in the Drumcondra suburb of Dublin, where integration is scarce, made for an outsider’s upbringing.

He did the same stuff as the other kids – played football, spayed graffiti around the city, tap-danced after school (“I’ll bust it out when I’m drunk, it’s mad funny”) – but he was always mindful of his heritage.

“I was really aware that I was different, always. My whole life. When I came to London I was like ‘what the fuck?’ It was so multicultural. That was crazy to me. I was always the black sheep.”

Did he suffer much racism? “It was more ignorance. I learned to understand that from a very young age. I’m numb to all that stuff. But it never got too hard. It was never ‘you’re really different’ – more ‘you’re different, but you’re still the same as us.’”

I wonder how much the struggle to fit in was behind him pursuing an art form not typically associated with Ireland. “Yeah, music was escape from it. That’s exactly how it was.”

So where does Alex end and Rejjie begin? “These days it’s the same person. Rejjie was always a different entity, but as the music got more personal, I am Rejjie now more than ever. I’ve killed off that character I made. In the future I’ll go under a different alias.” He smiles. “Just to keep things spicy.”

It seems Snow is reverting back to his true self. He says he wants to move back to Dublin when he has kids, and learn more about his Nigerian heritage. He is working on an autobiographical new album, Uncle Thomas, so he can "tell his reality". Whatever the guise he takes, the younger rapper is just getting started.

“It’s not my moment, y’know? That will be the next one. That’s how it feels. Artistically I’ve got more to offer. Now I can finally fly.”