Say what you like about Bobby Gillespie: he always returns a girl's calls.

The Primal Scream frontman may be renowned as a glam libertine with a penchant for pop's (un)holy troika of sex, drugs and rock 'n' roll, but confronted with an interview schedule that clashes with appointments and lunches, Gillespie keeps having to hang up the phone. He apologises each time and claims he'll ring back. And every time, he keeps his word.

But then Bobby Gillespie would never give up. The Glaswegian, once described by NME as our "Last Great Rock N Roll Star", has relentlessly helmed Primal Scream since he co-founded the band with Jim Beattie in 1982. Over 30 years and several line-up changes, Primal Scream have thrived as one of post-punk's most enduring, inventive and popular – not to mention controversial – products: a mob whose herculean appetite for hedonism and class As (now revoked) is eclipsed by their insatiable urge to excavate, politicise and rewire pop (sub)culture.

In doing so, Primal Scream have veered from C86 indie (1987's Sonic Flower Groove) to garage-rock (2006's Riot City Blues) via acid house, thanks to 1991's classic dance-rock rhapsody, Screamadelica, which bagged them the inaugural Mercury Prize. The band recently revisited Screamadelica with a 20th anniversary stadium tour, but they're always ones for moving on, and so it is that we find ourselves discussing their new album, London thoroughfares, society and how Gillespie likes his steak ("overpriced and undercooked").

Our conversation begins on a London cab journey which, in characteristic Gillespie fashion, swiftly becomes a political metaphor. "These roads are a nightmare," he says. "You used to be able to take a left into York Way from Copenhagen Street, but they've made it so you can't go left any more; you can only turn right." He doesn't miss a beat. "It's a bit like the political situation in this country. I think traffic jams are a great analogy for the way we live."

Primal Scream's 10th studio album, More Light, reflects upon, and rages at, the way we live. It does so via explosive social admonishments such as album opener 2013 – all kamikaze fanfares and ecstatic rock 'n' roll – but it also does so via intimate, shadowy elegies. It looks inwards and ventures behind closed doors, notably on epic blues requiem River Of Pain, which uncovers a cycle of family abuse through the eyes of a mother and child. Produced by cult-pop soundtrack maharishi David Holmes, and boasting such kaleidoscopic walk-ons as R&B soothsayer Robert Plant, The Fire Engines' post-punk activist Davey Henderson and free-jazz firebrands the Sun Ra Arkestra, More Light finds Primal Scream at their freewheeling finest: psychedelic, adventurous and raw.

The record's hallucinogenic sleeve design is by Turner Prize nominee, aesthetic comrade and former Boy Hairdresser Jim Lambie, and More Light is, claims Gillespie, an art album.

"Contemporary artists try to start a discourse on difficult subjects: they hold a mirror up to society and people's behaviour, way more than rock musicians do," he says. "It seems like we're living in a science-fiction novel where there's all this really bad stuff going down – whether it's corporate-driven free-market capitalism, or the governments that service that, or the wars that we're involved in, or just the general crushing of ordinary people – and nobody's protesting, even in a gentle way. There's no discourse, there seems to be no anger in culture. Everything's so conservative at the moment, it's like people make conservative art for conservative times. We wanted to do something a bit more f****** radical."

More Light revokes traditional song structures and defies musical boundaries, and its lawlessness evokes punk's insurgent spirit.

"To me, rock 'n' roll was always anti-conformist and anti-authoritarian, but now it seems everybody just wants to be part of the power structure, they all just want art as the capitalist dream," Gillespie says. "And I'm not against people making money and being glamorous – I love all that – but it just seems to me there's no music of protest. It's like people have been de-politicised; they don't have a political conscience."

Gillespie and co were raised in political households – does he think this instilled in them a sense of social responsibility? "Yeah, most of us have a political slant," he nods. "Andrew's great-grandad was involved with forming the Scottish Independent Labour Party, and he was a conscientious objector during world war one," says Gillespie of Primal Scream guitarist and co-songwriter Andrew Innes.

"Martin [Duffy, keyboards], his dad was a trade unionist, he worked in a car plant in Birmingham, and my dad was the general secretary of the Society of Graphical and Allied Trades in Scotland for most of the 1970s, so being politically active was in my family. But it's not like I'm trying to be like my dad. I just think anybody with any kind of consciousness of moral sensibility is going to be on the left, you know?"

For all of its typical Primal Scream touchstones – societal ire, rock 'n' roll swagger – it appears, from the title onwards, that More Light might reveal glimpses of something new. Gillespie agrees.

"We've normally got dark, aggressive, nihilistic titles like Vanishing Point, XTRMNTR, Evil Heat, Riot City Blues, and I didn't want another one of those," he admits. "The songs on the new record are dark, and painful, but they also have a real sense of tenderness. Even when it's violent or damaging subject matter, there's empathy for the characters in the songs. So the title was kind of coming out of that area of thinking, because you're shedding light on these things, you're sharing your hurt, and I think that might be cathartic and liberating for people. I think art should serve that purpose."

Gillespie credits Holmes for nurturing this new-found lyrical intimacy. "David really pushed me on this record and I broke through some barriers personally, and I'm kind of fearless now. That feels amazing at this stage in the game." The band's own knack for production, meanwhile, is as canny as ever. Previous albums have dexterously cast the Sex Pistols' Glen Matlock, Public Image Limited's Jah Wobble and Can's Jaki Liebezeit (among others), and More Light welcomes contributions from My Bloody Valentine's Kevin Shields (a some-time honorary Scream member) and Mark Stewart of avant-garde dissidents The Pop Group.

"When we bring people in, it's a production choice, it's as if we were making a movie," Gillespie offers. "If you were a movie director you'd choose the right actor to play the right role, and that's what we do. We wanted mournful, psychedelic, free-jazz, space-blues horn playing in the middle of River Of Pain, and the Arkestra were perfect for that.

"We wanted post-punk, spikey, fractured, discordant, abstract guitar for Invisible City, and there's no better than Davey Henderson. He's one of our favourite guitar players and favourite singers – we're big fans, we love Davey, we love [au courant pop deviants] The Sexual Objects and of course The Fire Engines."

And so Primal Scream's pop rebellion continues apace, resurrecting psychedelia, blues and post-punk while sounding more raucous and alive than ever. If anything, their music has become more ragged, more ravaged, as they've progressed – it's at odds with their 1987 debut, Sonic Flower Groove, which sounds incongruously polished. In a 1990 Melody Maker interview, Gillespie suggested they'd tried to be too perfectionist with that first record, that "it would have been much better if it had sounded rougher". Is that flawlessness something the band has actively railed against ever since?

"Yeah, you could well be right," he muses. "But also, I think the reality of the situation is that you get older [the singer is now 50 years old], you get better, and you realise that if you don't get it within the first couple of goes then either there's something wrong with the song, or there's something wrong with the band. And also, we were looking at Love, The Stooges, The Velvet Underground and thinking, 'Oh our first album's got to be as good as them, or else we're failures.' You have to learn to let go of that. You have to learn to lose the weight of history."

Or not. Since then, Primal Scream have elevated pop history – punk, blues, jazz – and effortlessly thrust it forward. Gillespie's steak arrives as we're musing upon this feat down the phone line, and he finally closes the lid on our chat. "Sorry again, but needs must," he laughs. "I have to eat, I'm on the run." That's More Light-era Primal Scream all over: ravenous, moving and rarely outshone.

More Light is released on May 13. Primal Scream play Glasgow Green (with The Stone Roses) on June 15 and Wickerman Festival on July 26

It seems like we're living in a science-fiction novel where there's all this really bad stuff going down and nobody's protesting