Dan Smith is of course as fed up as the rest of us with Theresa May, Boris Johnson and their partners-in-idiocy aboard HMS Brexit. But he’s also the tiniest bit tired of banging on about it constantly.

That he might be over his protest pop phase occurred to Bastille’s frontman at a festival in Germany in 2018, when the band’s multi-media show assailed an unsuspecting, up-for-a-good-time audience with a 30-foot image of “Theresa May in drag”. Sometimes he wonders what was going through his head.

“There had been a terror threat at the festival. The entire place was temporarily evacuated,” Smith recalls. “The next night, we got up and did our show. Behind us Theresa May is screaming along to a song called ‘Fake It’. We don’t not stand by it. But you can’t help think that the people at the festival would probably rather not be thinking about this shit.” Bastille were touring their second album, Wild World. As the title hints, it’s a proper sprawl, an unapologetically political affair that looks askance at a planet teetering on the brink (this was 2016 – how little we all knew).

But the group now feel they have very much been there and done that. Which is why they’re looking elsewhere — looking inward, really. This they do on follow-up Doom Days, a tighter, nervier excursion that, amid retrofitted rave beats, interrogates hedonism, late-twenties angst and a recent, hugely controversial move by Smith.

“I shaved my head in our video,” Smith nods, referring to the buzzcut he receives in the promo to lead single, ‘Quarter Past Midnight’. That is massively significant. At least it is if you belong to that segment of the British press which has long had fun poking fun at his bonkers barnet.

The hair and the lampooning has proved an occasional tender point for the otherwise very amiable Smith. This became clear when I interviewed Bastille backstage at Dublin’s Academy as their debut, Bad Blood, was blowing up in 2013. Immediately I felt I’d put my foot in something. “A journalist reviewed our album and made a comment about my haircut,” he told me then. As Smith said this, his head was spinning through 360 degrees and flames were jetting from his nostrils like one of those steam-punk contraptions you see at music festivals. The fire alarm may have gone off (it’s been a while; I’m slightly woozy on the details).

“I mean, are you really, in a broadsheet newspaper, making a comment about my hair? In an album review? How is that relevant?”

“It’s easy to over intellectualise these things,” he muses today when I bring up the “c” word (chopping his hair off).

“I wanted to shave it off for ages. It felt a little bit like starting from scratch, which was exciting. And, I guess, slightly provocative. We’ve never wanted to be that outspoken. We’re the types to keep our heads down. People latch onto what they can – so it’s, ‘Hey there’s that guy with the quiff’. Well, I don’t have it any more – so fuck off.”

Smith, you’ll have twigged, isn’t a typical frontman. He’s fidgety, thoughtful, self-contained. On stage, he doesn’t bask in attention so much as endure it politely. Yet far from a disadvantage, his reluctance, or inability, to preen is one of Bastille’s secret weapons. They’re the best sort of modern rock band. One devoid of swagger or machismo.

“Being on stage is not something I’ve thirsted for my whole life,” he says. “I do see myself as lucky to be up there. Getting up in front of thousands of people is an amazing privilege. I’ve hopefully got into it a bit more.

“Also times have changed: there’s an acceptance nowadays that you can be more human, flawed and fucked up. You can be honest about feeling nervous. We’ve built a career on being awkward weirdos.”

Smith began Bastille almost by accident. As a teenager, he was obsessed with cinema and wanted to be a director or movie editor. On the side, he wrote songs in his bedroom. These he kept secret until he was studying at the University of Leeds, when friends persuaded him to enter a songwriting contest. He agreed and placed second.

Fast forward a few years and Smith is in London, signing a deal with Virgin. In 2013, Bastille released the fourth single from their first album and everything changed. ‘Pompeii’ was a massive hit and quickly set a new record as the most streamed British single of all time. It also crossed to America, where it peaked in the charts at number four.

“We as a band have always been these weird outsiders,” says Smith. “There have been moments when we’ve had these Venn diagram crossovers with the mainstream. People have at different points seen us as an indie band, a rock band or a pop band. We don’t really give a fuck.”

Weirdly, Doom Days started life as a tribute to the rave scene of the ’90s. Smith’s too young to have actually experienced the rave scene of the ’90s. However, that once-removed borrowed nostalgia actually enhances the music, bathing the entire affair in a melancholy glow.

“I set out to make a throwback ’90s rave album that’s about pure hedonism,” says Smith. “But then it grew legs and wandered off. To go from writing about volcanos and Icarus [the essence of Bad Blood] to songs about the news and the elections and terror events to this… it’s quite a dramatic lurch. That’s typical of the band really.”

Doom Days’ concept of a long, lost night isn’t original, exactly. The disorientating thrill of life after dark is one of rock’s favourite subjects. Yet for Bastille the theme marks a significant break from their recent past.

“Both for ourselves and our audience it was a moment where we thought we could do with a bit of variety,” he says. “Our own sanity demanded it, really. It’s cathartic singing ‘Fuck you Donald Trump, fuck you Nigel Farage’. The thing is, that can’t define your every night. It made us react and want to write something different. Write something that was, if not positive exactly, then at least a temporary refuge from all of that.”

• Doom Days is out now. Bastille play Indiependence, Cork on August 2.