Brother Ali is sitting on the end of a couch in a dingy dressing room, backstage at the Garage in London. It's the final night of his European tour with labelmates Dilated Peoples, and he's desperate for a moment to himself before he goes onstage. He's eating dinner – something unidentifiable from a place down the street, smothered in a gloopy red sauce.

Dilated's frontman Evidence is in and out of the dressing room, trying to make arrangements for his flight back home the following day. "They had me flying from London to Atlanta, 11 hours!" he says to Ali. "Two-hour layover, then five-and-a-half hours back to California. Cost me $600 to change it, but now I can fly Air New Zealand direct."

Ali smiles in sympathy. He knows the score. When you're a rapper on an independent label, this is your life. You might be touring Europe, rocking sold-out venues in front of eager fans, but you still have to get your own food, eat in crappy dressing rooms, fight over flights.

Not that Ali and Evidence are complaining too much. The label they belong to, Rhymesayers in Minneapolis, is arguably the finest independent rap imprint in the world. It has been consistently better – for consistently longer – than any of the competition.

Other independents have folded, split, been absorbed by outfits with bigger pockets and bigger appetites, but Rhymesayers has just kept on trucking. It is a label built on struggle: a place for brutally honest rap music that has captured the ears of thousands upon thousands of fans. Its artists don't shy away from difficult topics, rapping about drug abuse, broken homes and alcoholism. Rhymesayers is based in a city that was never regarded as a hip-hop stronghold, and it has worn the underdog patch on its sleeve proudly.

Rhymesayers rests on the bedrock of its flagship act, Atmosphere – its members Slug (Sean Daley) and Ant (Anthony Davis) co-founded the label in 1995 with buddies Musab Saad and Brent "Siddiq" Sayers. In 1999, they opened a record store, Fifth Element, and the label and shop still share the same office space in uptown Minneapolis. For the past five years, Rhymesayers has taken over Canterbury Park in nearby Shakopee for Soundset, a festival that drew 20,000 attendees in 2013. It would be wrong to say the label was the starting point for Minnesota hip-hop, but it has paved the way for everyone else. Today, the city has a furiously bubbling music scene, including crews and MCs such as Doomtree and Dessa.

Reading on mobile? Click here to watch the video for Atmosphere's Guarantees

Rhymesayers has three dozen artists on its roster, from Atmosphere, Ali and Dilated Peoples to the ultra-complex rapper Aesop Rock and former Jay-Z affiliate Freeway. MF Doom released his classic Mm .. Food on the label. Sales are solid, even though – as Ali says – "It still operates outside of the music industry. There are music-industry connections, but it's still the guys in Minneapolis doing it."

Dilated Peoples' Evidence (Michael Perretta) is a recent signing. Known for his laidback, monotone flow, he has also become recignised for his amazingly good Instagram account – his mother was a photographer, and he enjoys documenting his travels. In most of the interviews he does, he spends as much time discussing photography as he does music.

Ev is from Los Angeles, far from frigid Minnesota, but he's had such a good experience with the label he convinced the two other members of Dilated to sign on – their album Directors of Photography is out in 2014. He knows and understands major labels and independents; he and his crew were previously signed to Capitol Records. "It's one thing to imagine it, but I've actually experienced the differences," he says. "I've experienced what it's like to have a lot of money behind you and go to radio and MTV and Top of the Pops, NME showcases. Then there's being independent, which is a reality check. Rhymesayers is the highest level of independence I've ever experienced. I might not have as big a budget, but I'll go out and get it."

Ali (born Jason Newman) is a Minneapolis local. On Rhymesayers, he's second only to flagship act Atmosphere. He's legally blind; an albino Muslim with the voice and on-stage persona of a revivalist preacher. Away from the crowd, he carries himself with an almost eerie calm. When he says that chart-topping indie rappers such as Macklemore (whose independently released Thrift Shop was one of 2013's biggest songs) and Kendrick Lamar should give credit to Rhymesayers, you believe him.

"People don't see Kendrick Lamar and Macklemore as being related to Atmosphere, but they are," he says. "There are businesspeople who learned what Atmosphere did – both musically, in terms of how you express yourself in song in a way that's still respectable and doesn't imitate traditional rap, and in terms of [running a label]. Macklemore learned a whole lot of that – the approach to … doing business, touring, making heartfelt music.

Reading on mobile? Watch Brother Ali's video for Uncle Sam Goddam here

"I would like it if they would give credit to Atmosphere. Because the world – that world – doesn't know Atmosphere. In a way, they're getting credit for [what we did]."

Later on, we call up label head Siddiq at Rhymesayers' headquarters. He doesn't agree completely with Ali. The idea of an independent label, he says, didn't come from them. But even though he admits that, 18 years after it was founded, the label still faces some uphill battles, he knows why it's still around. He speaks about Def Jux, a New York label run by rapper-producer El-P, under the slogan "Independent as fuck". Def Jux folded in 2010.

"[It was an] amazing label, with amazing creators, doing amazing work," Siddiq says. "But I'd say that they all had a similar sound. That came from El-P helming the ship and driving the production. It made it a crew thing, and they had a similar sound. With us, I always wanted it to be more like a Def Jam. You might get an Atmosphere, a Freeway, MF Doom, Ali – they don't sound the same. I wanted the label to have that diversity."

Rhymesayers is expanding – it has recently signed two more local acts, rappers Dem Atlas and Prof. Evidence is going to be busier than he's ever been: not only will he have to contend with the first Dilated Peoples album in five years, but he's also on the verge of releasing Step Brothers, a collaboration with heavyweight producer Alchemist. Atmosphere – quiet for the past two years – have been making noise about a new record, and have just reissued their album Seven's Travels on vinyl.

"Truthfully?" Siddiq says. "There was no goal when we first started this. We were just a bunch of young cats who were into hip-hop. We were just living it."