When Douglas MacInytre founded The Creeping Bent Organisation to release records in the art/ pop spirit of the Edinburgh-based Fast Product label Glasgow's Postcard Records, he was asked in an interview who his influences were.

His reply namechecked Fire Engines, Suicide, Subway Sect and The Pop Group, musical agent- provocateurs all, who in different ways, defined what came to be known as post-punk.

At the time, MacIntyre had never met any of the artists concerned. Now, with Creeping Bent about to enter its 20th year of operations, it's a different story: the label has put out material from key players of all the acts named. These include Davy Henderson's post-Fire Engines projects The Nectarine No 9 and The Sexual Objects; Alan Vega of Suicide's collaboration with producer Stephen Lironi as The Revolutionary Corps Of Teenage Jesus; and Subway Sect founding father Vic Godard's live forays with Bent mainstays The Leopards and The Sexual Objects. There have also been a couple of underrated albums by Pop Group guitarist Gareth Sager.

It is with a reformed Pop Group that Creeping Bent begins its year of celebrations, with the band's first Glasgow gig for 33 years forming what might be the most adventurous show in the 2014 Celtic Connections programme. For MacIntyre, the event is a dream come true.

"There's something about that first Pop Group single," MacIntyre says of the band's 1979 release, She Is Beyond Good and Evil. "After Anarchy In The UK, it was a massive record for me, and it's still an amazing piece of art. It opened up a whole world, from the Nietzsche reference in the title, to reading interviews with them talking about free jazz. I'd probably never heard of either of those things at the time, so it was almost like your university."

Given that The Pop Group were still in their teens when they formed in Bristol, they too were learning their chops. Even so, She Is Beyond Good And Evil remains an intense and incendiary musical hand-grenade that pitted Mark Stewart's sooth-saying vocals against Gareth Sager's slash-and-burn guitar, all bolstered by a rhythm section fired by funk, dub and jazz at their most elemental.

"In Bristol everyone went to the same nightclub," says Edinburgh-born Sager, "so you'd have half an hour of punk, half an hour of funk, half an hour of jazz, and it was small enough to be able to create your own scene."

Sired in the heat of the recession that would usher Margaret Thatcher to power, The Pop Group's urgency was heightened by the potency of Stewart's apocalyptic-sounding lyrics. "I was haunted by the disasters of the century," Stewart says today. "Grief, anger, terror and loss beyond words."

This attitude was made even more explicit on The Pop Group's second single, We Are All Prostitutes, and on albums, Y and For How Much Longer Do We Tolerate Mass Murder. After touring with The Slits and jazz trumpeter Don Cherry, the band imploded in 1981. While original bass player Simon Underwood had already joined a nascent Pigbag, his replacement Dan Catsis joined Maximum Joy with The Pop Group's second guitarist, Jon Waddington. Sager and Pop Group drummer Bruce Smith, meanwhile, formed anything-goes skronk troupe Rip Rig And Panic with a line-up that included Don Cherry's 16-year-old stepdaughter Neneh on vocals. This left Stewart to join forces with producer Adrian Sherwood and Sugarhill Records' in-house band, rebranded as The Maffia.

Such a multicultural Bristolian legacy has trickled down through Massive Attack, Tricky and Neneh Cherry's recent collaboration with Scandinavian jazz power trio The Thing, all the way to the reformed Pop Group's 2011 appearance at the Portishead-curated I'll Be Your Mirror event in New Jersey.

When they arrived on the scene, the likes of The Rapture and assorted other American bands had clearly heard a Pop Group record or two, while the current line-up of Stewart, Sager, Catsis and Smith were recently made aware of a compilation of Polish bands covering Pop Group originals. Its name? Still Tolerating Mass Murder. As global unrest mounts, it seems, The Pop Group's time is now.

"I remember the first time I went to Optimo," MacIntyre says of Glasgow's Sunday night leftfield clubbing institution. "I was coming down the stairs, and I heard a Pop Group record playing - I think it was Where There's A Will There's A Way - and there were all these art school groovers dancing to it in a way that no-one ever did first time round. And I thought, 'This is it'."

Since reforming in 2010, The Pop Group have kept their fiery spirit alive, even as they've reclaimed their legacy without ever succumbing to mere nostalgia. As Sager points out, "Nobody would think twice about going to see Miles Davis when he was 65 as long as he was doing the business. It's only our culture that has this weird age thing. But look at Don Cherry. That guy was a groover."

With recordings of new material ongoing when logistics will allow, Stewart, at least, is on a mission.

"In the studio recently we released a Golem," he says, "and I can simply sit back in awe. We are bristling with visions of a both terrifying and glorious future which is ours."