The evening before we’re due to meet, Duglas T Stewart gets in touch with a warning. Over the last two years, says the frontman of BMX Bandits, he has been wrestling with mental health issues that manifest themselves in self-harm. “Last night,” he explains, “I attacked myself – and my face got a lot of it.” Despite the fresh cuts and scratches across his cheeks, nose and forehead, he still wants to meet up and talk about the 30th anniversary of his band. “It’ll be good,” he says. “Laughter and tears.”

Laughter and tears. Both have been reliably provoked by BMX Bandits since theirdebut single, E102, in 1986. And anger, too – as well as confusion, joy and even envy. Kurt Cobain said that if he could be in any other band, it would be the Bandits. Oasis, when starting out, were their support act. They are, perhaps, Britain’s ultimate cult group and its most divisive. Some see them as nauseatingly cutesy and affected, others as creators of supremely sophisticated, witty love songs.

At the centre of this contradiction is Stewart himself, an amiable 51-year-old man-child. The intercom to his Glasgow flat has two intertwined hearts on the button. He buzzes me in. Deep breath. Here we go. “Hello,” he says, shaking hands. “Come in.” His face looks sore, but not too bad. He sits down on his sofa and leans against an emoji smiley cushion.

Stewart won’t say what caused him to hurt himself, other than that it’s to do with a relationship. Twice married, with a 21-year-old son, his life could be seen as a quest to find perfect love – and to turn it into a perfect pop song. “Love and art are, for me, the two things that are important in life,” he says and his romantic life has always fed into his work. “I don’t think I can take it much longer / She said maybe your tablets should be stronger,” he wrote in Serious Drugs, the band’s best known song, inspired by a girlfriend’s suggestion that he up his dose of antidepressants.

“It’s strange,” he says. “I never had an experience of self-harming until I was close to 50.” When he feels rage and sadness, he directs them at himself rather than at those who have triggered them. “I think it’s related to why a lot of people like myself choose to become artists. Creating beauty out of pain and ugliness has been a big part of what I’ve tried to do. I can make things make sense in a song that don’t make sense in the real world.”

One thing that makes little sense is that BMX Bandits have not had the wild success they deserve. Stewart’s ear for melody and flair for lyrics make for immaculately crafted songs. He’s a sort of bedsit Bacharach. Yet there is something of a comedy of errors about his own career. Three albums on Creation in the 1990s seemed to promise success, especially with the single Serious Drugs. “That was hilarious,” Stewart smiles. “We had all these people at Radio 1 saying they loved it and it was going to be big, but its release coincided with their anti-drugs week and they couldn’t play it.”

Radio playlists weren’t their only difficulty. BMX Bandits were an awkward fit with the laddishness of Britpop, just as they had been too sunny for po-faced post-punk. Their most recent album, 2012’s BMX Bandits in Space, was their best-selling since the Creation years, but the general trajectory has been one of mass indifference mixed with intense devotion from those fans who consider themselves privy to a delicious secret. In any case, the idea of music as a “career” is not one Stewart would recognise.

To all intents and purposes, he is BMX Bandits. The lineup has changed many times. Musicians come, go and come back: “We’re like Hotel California. You can check out any time you want but you can never leave.” Stewart describes the group, currently a six-piece, as a musical family, but it seems to function more like a shield, protecting him from the sad realities of life. He always had a strong sense of who he was: a rather flamboyant figure called Duglas (he dropped the “o” in his late teens). But lately, he says, he has lost touch with that identity, and now feels he’s simply treading water. Only when making music does he feel like his old self. “Playing live has become more important than ever,” he says. “I feel like every atom in my body is alive again.”

The new album Forever, due in spring, was partly recorded in this flat in Glasgow’s south side. Stewart moved here last summer after spending most of his life in Bellshill, the post-industrial town 12 miles to the south-east. If you want to understand the Bandits, you have to visit Bellshill, so we drive over, parking near where Stewart grew up on Ramsey Wynd, a terrace of pebble-dashed houses on a council estate. He points out the bedroom where they came up with the name BMX Bandits.

Early lineups included Teenage Fanclub’s Norman Blake, a friend of Stewart’s since before school, and Sean Dickson, later of the Soup Dragons. In Serious Drugs, the 2011 documentary about the Bandits, Blake recalls going round to Ramsey Wynd to record songs on a cassette player. Lacking drums, they would hit empty margarine tubs with pencils.

Stewart’s best friend and next door neighbour was Lorna Gibb. In The Two Gardens, a memoir published by Granta, she recalled the estate in the 1970s and early 80s as a place of sectarian violence, unemployment and heavy drinking. Fights would leave blood and broken glass on the communal patch of grass out the front. Gibb recalls Stewart wearing “weird clothes and makeup, even though he was a boy when boys were not supposed to do that kind of thing; we were fair game for bullies”.

Stewart and his big sister Alison would stare down from their bedroom at the fighting. He felt secure in this home, with parents who never argued: they had that perfect love he has sought ever since. He remembers his father singing to his mother over the kitchen table: “Come into my arms, bonnie Jean.”

From early childhood, Stewart was a performer. He’d tour the classes at primary school, singing, telling jokes and doing impressions. At secondary – Bellshill Academy, a red sandstone building with the motto Virtus in Arduis, courage in adversity, carved above the entrance – a trendy geography teacher turned him on to Jonathan Richman. “I like art that bypasses the intellect and goes straight to the heart,” he says.

Sheena Easton was in her final year at the school when Stewart was just starting. He saw her as a kindred spirit. “She looked like she’d already decided, ‘I’m somebody.’ I don’t think that was arrogance – it was just that she knew she wasn’t a normal person.” Stewart stood out too. When boys gathered for furtive cigarettes, he would turn up wearing a deerstalker and smoking a pipe. He introduced himself to bullies as “Nancy”. He was the only boy in school allowed to wear earrings, having secured a special dispensation from the art teacher on the grounds that it would be a shame to stifle his creativity.

Glasgow began to exert a gravitational pull. To earn money to buy records, the embryonic BMX Bandits would busk for shoppers. They also played at Bellshill’s Hattonrigg Hotel, no longer there, and discovered that their anti-macho image could be provocative.

“A group of punks decided to protest,” says Stewart. “They were all sitting outside saying, ‘Don’t go into this gig.’ Like a picket line. I couldn’t understand why they found us objectionable, but I liked it. Another time, a bunch of skinheads turned up, and Norman and I decided we’d do the Dead Kennedys’ Nazi Punks Fuck Off just to see what happened. They all came down the front, signalling they were going to cut our throats. The police were called and escorted us out the back.”

In 1985, he discovered a Glasgow club night full of like-minded musicians and artists: Splash One. “Suddenly the weirdos and outsiders had a place of our own. It was like a collective brain.” Run by the young Bobby Gillespie, among others, Splash One was a crucible of influences where the chat was all about music, cinema, art, punk and psychedelia. It only lasted for a year, but continues to shape Scottish culture.

Stewart is no nostalgist, however. He is an evangelist for up-and-coming Glasgow bands such as TeenCanteen and Happy Meals – and he certainly considers BMX Bandits a contemporary group. “I’m alive when I’m in the BMX Bandits,” he says. “I’m alive even when I’m talking about the BMX Bandits. Life can be very difficult. But when we’re on stage, when I’m in that world, everything is OK.”