Glasgow will always have a place in the hearts of art-pop trailblazers Cornershop.

"We were in Glasgow when we found out that we'd gone to number one," remembers co-founder Ben Ayres of their kaleidoscopic 1998 chart-topper Brimful of Asha.

"That became a hazy memory very quickly," he laughs. "We genuinely didn't realise, or even consider, thatwe'd be at the top of the charts that day. But then our label man at the time, Gary Walker, who ran [indie label] Wiiija, turned up at the hotel and said, 'Guess what?' And that was it."

We have many reasons to be thankful for Cornershop, who formed in 1991 and count Prince, Johnny Depp and David Byrne among their fans. They upended cultural stereotypes. They defied Britpop's account of our UK rock lineage and its customs as principally white. They augmented the indie-dance toolbox with instruments like the tamboura and the dholki.

Norman Cook's remix of Brimful of Asha is also of historic note: it overthrew the chart reign of Celine Dion's murderous ballad, My Heart Will Go On. "Haha, yeah, I think we did everyone a bit of a favour with that alone," says Ayres.

It was not the first time Cornershop had waged battle on the pop aristocracy. They made music press headlines in 1992 by setting fire to a Morrissey poster outside his record company (EMI), enraged by racially provocative tracks like National Front Disco and Asian Rut.

"Three Asian kids and a white kid from Leicester, ex-Morrissey fans all, clasp indie music to their bosom and prove there's more to Asian pride than bhangra", raved Melody Maker at the time, under a shot of the ceremonial Moz torching.

Cornershop's music was similarly incendiary – exotic, nostalgic and politically-charged – as evinced by their explosive (and ramshackle) early live shows, and a series of wayward releases like their 1992 debut EP In the Days of Ford Cortina (ever ones to exploit pop-as-social-conduit, they released it on curry-coloured vinyl), and their 1995 magnum opus, 6am Jullandar Shere.

The latter's inclusion on 2001's Rough Trade 25 Years Box Set highlighted Cornershop's enduring – and dazzling – versatility. Amid a variegated track-list that included the Sugarcubes, Pixies and Aphex Twin, their Punjabi-psyche guitar mantra sounded unlike anything else.

"When we first started out, it was quite a challenge for any community that we played to, whether that was white or Asian," recalls co-founder and singer-songwriter Tjinder Singh. "They couldn't really stand it, either of them." But Cornershop's Indian-tinged dance-rock was not wilfully anomalous – it celebrated, excavated and fused the myriad sounds of Singh's childhood.

"The first music I listened to was Punjabi folk music and Sikh devotional music," says Singh. "I didn't really listen to pop music until I was eight or nine. After that, it was a case of slowly collecting the records that my parents never had – The Velvet Underground; The Beatles; stuff I discovered through my brothers. My oldest brother was really into heavy metal, God bless him, but it was my middle brother who got into music that was saying something a bit different."

Cornershop have always utilised art as a means of political expression. Has this impulse, or this sense of social responsibility, relaxed since their days as angry young men? "No, I think it's always been the same," offers Singh, "whether we do it with sounds, instrumentals, songs or collaborations.

"There's a lot of different ways that you can be critical," Singh continues. "Whether it's a reflection on the music industry with Who Fingered Rock 'N' Roll, or that Asians can sing about Christianity with The Turned On Truth [both of which featured on their 2009 album, Judy Sucks a Lemon for Breakfast], or whether it's just to get people to stop in their tracks by doing an album in Punjabi."

The Punjabi album to which Singh refers is last year's Cornershop and the Double-O Groove Of – a terrific collaborative LP with Punjabi folk singer Bubbley Kaur, and a seven-year undertaking which bore nascent fruit with the beatific groove of 2004's Topknot. "The Bubbley collaboration was very much a studio rather than live project so we've no plans to take it on the road," explains Ayres. But he promises many alternative pop thrills from their imminent Glasgow show.

"We'll be playing tracks from Judy Sucks a Lemon- which we've never performed in Scotland, plus material from across our career," he says.

It's testament to Cornershop's ongoing relevance and creative drive that they've a two-decade cult-pop trove from which to mine, including albums like 2002's Handcream for a Generation (which starred another fan, Noel Gallagher) and 1997's Mercury-nominated When I Was Born for the 7th Time (which featured a collaboration with Beat-guru Allen Ginsberg). "Yeah, when we started out we used to make fun of the fact that Status Quo were always saying, '25 years in the music business!', but it's actually coming up fast for us now," Ayres laughs.

What of those youthful indie-punks who incinerated Morrissey's image? "I'm proud we stood up for what we believe in. We were all huge fans of The Smiths, but at that time it seemed no-one else was prepared to actually say loudly what many people were feeling, so we stood up and made the point," says Ayres.

Would they do it again?

"You have to do what you think is right, don't you? I'd do it again in an instant."

Cornershop play Platform, Glasgow on Friday, January 20 as part of Celtic Connections. For Cornershop records, history and more, see www.cornershop.com.