IF Glasgow long ago passed the tipping point whereby it stopped being a place creative people left in order to further their careers and instead became one they moved to for the same reasons, then I'd argue it has The Pastels to thank.

They, after all, are the band who stayed, setting an example to – and a template for – groups like Teenage Fanclub, Mogwai, Belle And Sebastian and The Delgados, who all found critical acclaim and international recognition but on terms that involved no change of locale.

And if a city produces a new generation of bands every three years or so, then The Pastels have seen 10 or more such generations come and go since they released their first single in 1982. That, by the way, was the same year Paul Weller disbanded The Jam.

Don't think that dates The Pastels or their music, though. Their second album Sittin' Pretty may have been released as the Madchester scene swept all before it in 1989 and their third, Mobile Safari, as Britpop reached its height in 1995, but the Glaswegians have always stood at a remove from the prevailing musical orthodoxy. Gloriously, defiantly so, in fact.

Today, three decades on from his first foray into recorded music, founder and Pastel-in-chief Stephen McRobbie also runs a record label, Geographic, and a record shop, Monorail, located in the rear of vegetarian cafe Mono. It's here we meet to discuss album number five – Slow Summits, out next week – and take a spot of lunch.

The Pastels released their soundtrack to David Mackenzie's film The Last Great Wilderness on Geographic in 2003, and in 2009 returned to the studio to collaborate with cult Japanese duo Tenniscoats on long-player Two Sunsets. But, on paper at least, it's been 16 years since their last album proper, 1997's Illumination. Did McRobbie think then that there would be such a hiatus?

"Certainly not. I think I'd have felt completely despondent at the idea that so much time could pass," he says, before explaining the reasons: after a final couple of Peel sessions in the late 1990s, longtime member Annabel Wright left to concentrate on her art and McRobbie and remaining member Katrina Mitchell threw their energies into Geographic, set up for them in 2000 under the auspices of Domino Records as a sort of independent fiefdom of musical cool.

Then, two years later – and in part because he was irked at the unavailability of Geographic releases in Glasgow stores – McRobbie set up Monorail. Small but perfectly curated, it had its tenth birthday last year and regularly finds it way into lists of the best independent record shops. Even a cursory flick through its treasures makes it easy to see why.

Slow Summits was recorded in Glasgow by John McEntire, mainstay of acclaimed Chicago band Tortoise and a longtime friend of The Pastels. The core of the band is McRobbie and Mitchell along with Tom Crossley, John Hogarty, Gerard Love of Teenage Fanclub, and Alison Mitchell, Katrina's sister. Also on board are Love's Teenage Fanclub bandmate Norman Blake; a returned Annabel Wright; Stefan Schneider and Ronald Lippok from Berlin-based post-rock band To Rococo Rot; and – tearing himself away from his work on Baz Luhrmann's film adaptation of The Great Gatsby – feted soundtrack composer Craig Armstrong.

Armstrong's contribution came about when McRobbie asked him to choose a film for a regular movie evening Monorail hosts at the Glasgow Film Theatre. "We were talking in the bar afterwards and he said 'If you ever want some strings in a track, don't feel you can't ask me'." Taking him at his word – and grateful for Armstong's refusal of a fee – McRobbie asked him to score the track Kicking Leaves, a wonkily gorgeous love-song.

"I wasn't surprised about working with Craig," McRobbie adds with a smile. "I thought it would be something that would happen sooner or later."

That belief that everyone swimming in Glasgow's rich pool of talent will eventually cross paths and make art/music/whatever is an important one. It points to a strong sense of (and belief in) community, and for McRobbie that's what The Pastels have always been about more than anything else.

"An important thing for me, and something we got from our parents and grandparents, was the sense that Glasgow was a socialist city. I always wanted the music that I made to have its own identity but we were also looking to be part of a community," he says.

It was that belief in community and in Glasgow's "possibilities" – his word – that kept him in the city. "We were one of the first significant groups in the 1980s to stay. Up until then most groups moved to London, so there was never any sense of things becoming more solid.

"Postcard was enormously exciting but very brief and it never really transformed things. If Orange Juice had stayed, Glasgow might have transformed a lot quicker. But when we started, it was kind of grim. There wasn't," he adds, looking around him at the young urban hipsters eating lunch with their MacBooks open, "anything like Mono."

His first efforts as a label boss play to that same idea. In the 1980s, with label 53rd & 3rd, he released early singles by Edinburgh band The Shop Assistants and by local acts The Vaselines and The Boy Hairdressers, who would transform into Teenage Fanclub and who featured future Turner Prize nominee Jim Lambie (on vibrophone, at one point). Later, with Geographic, his world view expanded and he became evangelical about acts such as Maher Shalal Hash Baz, the alter-ego of shadowy Japanese musician Tori Kudo.

But, importantly, it was from Glasgow that he launched Kudo's music in the west and to Glasgow that bands such as Tenniscoats came to perform and record.

"I had two opportunities to do record labels and I knew it was important to take them otherwise a lot of music I thought was great would go undocumented," he explains. Plus, he says, "it's good for musicians to understand things from all sides. It can be an over-precious existence otherwise. It's good to know how things work."

The music of The Pastels, and of many of the bands who have followed in their wake such as Belle And Sebastian, is often described as sweet and melodic but with an inbuilt looseness to which you could add descriptions like "lo-fi", "woozy" or "naive".

Those who love it, love it; those who don't (far fewer in number) perceive it as contrived or artfully gauche. They may even use the word "fey". So does McRobbie see The Pastels' music as standing in opposition to the usual cliché about Glasgow – that it's a violent, aggressive, gallus place – or does he think it simply articulates something else in the city's DNA, something which is gentler and more hidden from view?

"We always gravitated towards something melodic and hopefully optimistic, but I do think our music was mostly balanced," he says by way of an answer. "I never lived in schemes so I didn't feel I could talk about it or particularly wanted to. But for me a filmmaker like Bill Forsyth has that balance – there's something hopeful about Glasgow but you're aware it's not coming from rich, advantaged people."

McRobbie says he felt pride when he heard political songs like Special AKA's Free Nelson Mandela and Robert Wyatt's Shipbuilding, but he always knew "it was something I couldn't do."

He adds: "It just wasn't my role as a writer. So you write what you feel has a truth to you. The Pastels were never sloganeering."

That said, there always was grit and muscle at the heart of the band's sound and "almost everyone who's ever been in the group has always been very clear-minded about their politics. People always knew what they were about and could articulate it."

The Pastels are a Glasgow institution, then, and so, it seems to me, is Stephen McRobbie. I finish by asking him if he's comfortable with that label. His answer is typically modest.

"Because we've been around a long time, we occasionally get asked for advice," he says. "But I think it's really dangerous for an artist to get bogged down in their own baggage, or their own sense of self-importance. We're all dots that together can become something really beautiful and fantastic - If we weren't there, things would still be really strong."

Somehow I doubt that.

Slow Summits is released on May 27 on Domino. The Pastels play CCA, Glasgow on June 1