If you can say one thing about Young Fathers, it’s that they’ve always been confident in their ability to create groundbreaking music. The three members of the Scottish experimental hip-hop trio – Alloysious Massaquoi, Kayus Bankole and Graham “G” Hastings – met in 2001 when they were just 14 at Edinburgh’s under-16s Bongo club.

“Afterwards, the guys started coming to my mum’s house to record music,” Hastings tells me when we meet to discuss their extraordinary year. “I didn’t know how anything worked. I had a £10 software system that made beats and I used to burn those on to a CD, and then put it into a karaoke machine that we’d sing over. Later, we’d walk to the bus stop singing the songs and imagining the videos. Even then we thought they were hits!”

Though Young Fathers have been compared to a variety of artists, from Kanye West to MIA and Massive Attack, it’s hard to describe their sound in one sentence. They say that they take hip-hop and pop and “dip them in a tie-dye mix of Ronettes and krautrock and ragga and dub and post-punk and Afro-psych”. It’s a recipe that’s proven successful: in June, the band’s second mixtape, Tape Two, won the 2014 Scottish album of the year award; in October, their debut album, Dead, overcame 14/1 odds to win the Mercury prize, beating competition from FKA Twigs, Kate Tempest and Damon Albarn.

“The fact that we came together in a place where there’s not really anything happening probably had an effect on us as a band,” Hastings continues. “You push the envelope a bit more because there’s no scene to get stuck into.”

When I ask them about the Mercury, they say their main focus going into the ceremony was the performance rather than the nomination.

“People back home were going to watch us on TV, but there was an audience of industry folk who probably haven’t been exposed to a band like us before. Win or lose, we’d already won,” Massaquoi says. “I saw the excitement in my parents’ eyes and it made me feel proud to be in this group.”

But the band wound up the press because of their nonchalant response to the win, as well as their refusal to speak to any rightwing papers. How did it feel to amass a batch of negative press cuttings?

“Winning an award and talking to the press on the red carpet is part and parcel of the industry – we have no problem with that,” Massaquoi clarifies. “But most of the stuff we said wasn’t used. They said we never smile. I don’t understand, I’m smiling now” – at this point, the three of them beam at me – “all it boils down to is they want you to play ball. They judge us because they think we should be grateful but we deserved to be there. The Mercury is about innovative music. If we hadn’t won it, it would look bad for them.”

The trio have never been afraid to take a stance – they have a song called Queen is Dead and last year played a refugee benefit gig in Scotland, which Massaquoi says was particularly “personal” for him, having emigrated to Scotland from Liberia as a kid. Would you call yourselves a political group, I ask.

“Political bands bore me,” says Massaquoi. “The sentiment behind them is always good, but it’s just like, ‘I know about that. I read the news. Why don’t you take me somewhere else?’”

“We’re consciously aware of our environment but we’re not a conscious band,” Bankole interjects.

Despite this, Young Fathers say that there are various issues they want to address in their music. “Obvious things about what’s happening all across the world,” Hastings says. “Unjust wars, money being spent, the rightwing press’s anti-immigration rhetoric, Tory fucking shite that they’ll never admit to. But we try and fit all that into a pop song. That’s the kind of music I listened to growing up – Peter Tosh, Marvin Gaye. After all, music is not some robotic thing. It stems from the soul, from a place inside. Otherwise, it’d just be a maths equation.”

With a UK tour, a US tour and a new album in the works, next year looks like it will be a busy one for Young Fathers. Is there anything in particular that they’re hoping to achieve?

“We want our music to be worldwide. We believe that this kind of music should be recognised and seen,” says Massaquoi.

“Making music has become a necessity,” Bankole adds. “We’re never clocking off. Every single day, from waking up to going to bed, we’ll be thinking of the music we’re making.”