Cinematic strings, chanson and cabaret, folk ballads and flamenco, filtered through Scott Walker, Del Shannon and Calexico. Take all this then imagine it being played by five cheerful Glaswegians who have been in and around the city's music scene for 20 years and you start to get an idea of just how special A New International are.

Formed from the ashes of cult favourites the Starlets, a band who shared the stage with the likes of Belle and Sebastian and Camera Obscura, A New International have been quietly building a devoted fanbase in Scotland and Europe for the past 18 months.

Debut album Come to the Fabulon received glowing reviews from the likes of Times music critic Pete Paphides and Richard Hawley on its release in March, while the band's recent BBC radio sessions and live shows – including a gig at the CCA in Glasgow described by Deacon Blue's Ricky Ross as "magical and dangerous" – have ensured cult status for the second time.

The magic Ross refers to comes from the musicianship and the ambition of the songwriting, with resulting soundscapes that are lush and romantic, complex and multi-layered, all built around charismatic frontman Biff Smith's remarkable vocal range, acoustic guitar and accordion playing. Brooding electric guitars, violin and trumpet add texture, harmony and depth.

Though the band are still playing small venues, this is a sound and attitude that would work just as well accompanied by full orchestra in the big concert halls, and the increasing buzz around A New International suggests a bigger stage and wider recognition are just around the corner. It's no less than this talented bunch deserve.

After all, there aren't many bands that have the imagination and confidence to completely recreate themselves in order to have a second bite at the cherry. And according to Smith there are advantages to being a bit older and wiser."I think the band know one another, and ourselves, well enough by now to be able to recognise our strengths and to accept what we are less good at," the 43-year-old smiles philosophically. "We're more of a team now than in the past.

"I suppose on the way to here some members have, in the traditional sense, grown up more than others, having 'proper' jobs and families with all the attendant responsibilities, so it's not as easy to pack our guitars and go off on an adventure as it once was. Our time is limited, but so is everyone's – that makes it more precious."

Smith says that although the band is staunchly internationalist in outlook, Glasgow has long been both a muse and an inspiration.

"I love anything which doesn't know its place or obey the rules in art, love, literature, music, life," he explains. "Cities act like magnets to kids growing up in the satellite towns and surrounding areas. I grew up in Cumbernauld where everyone's parents were not only from and born in Glasgow but also spoke about the city as though it was still there, just outside the window.

"I have visited some stunningly beautiful cities which didn't quite seem to me to have the cultural vibrancy of Glasgow. Perhaps we create something because we have to. Although there are many areas of beauty in Glasgow, it is not a looker of a city in the way that, for example, Paris, Prague or Edinburgh is, so perhaps we try harder, have more to prove. Glasgow in winter can be an endurance test, so we make things, paint things and write things to cheer ourselves up."

Smith believes there is at least another album in the current line-up, and after that, well, who knows? In the meantime, if you want to experience the spine-tingling pop perfection of A New International up close and personal, get along to one of their forthcoming Scottish shows. The secret is almost out.

A New International play Glasgow's Glad Cafe on January 26. Come to the Fabulon is out now

Read more: our Hot List 2016 arts picks including David Bowie and Outlander's Richard Rankin