Shortly after The Twilight Sad left the stage at the Hollywood Bowl in Los Angeles in May 2016, frontman James Graham received a text message. It was The Cure’s Robert Smith, who had personally invited the Scottish group to support the bed-headed goth icons on their US tour. Hollywood Bowl was opening night and, with an A-lister-stuffed guestlist, The Cure did not lack for celebs with whom to enjoy post-show selfie moments.

“He asked us did we want to go for a drink after the gig,” recalls Graham. “He was like, ‘I don’t want to hang out with all those people. I want to hang out with you.’ He’s at a point in his life where he just wants to hang out and shoot the shit and talk about music. We treat The Cure like normal people. They don’t always get that and I think they appreciate it.”

Criss-crossing America with The Cure was, of course, an experience. The Twilight Sad performed to enthusiastic audiences but also to rooms who had no idea who they were.

“Because you’ve got Robert’s seal of approval they will give you a chance,” says Graham. “They trust him – so you’re going in with a head start. We did three nights at Madison Square Garden. It was amazing.”

Big name bands aren’t always supportive of their opening acts, as The Twilight Sad have previously discovered. For The Cure to be as accommodating as they were was a bells-on bonus.

“With some artists you are the support and you never even see them. You’re just the opening act. The Cure treated us like family. We hung around a lot with Reeves Gabrels, who is in The Cure now and used to play with Bowie [and was a member of the Thin White Duke’s ill-fated Tin Machine – Bowie ed]. You had to pinch yourself – I’m backstage talking to Reeves Gabrels about Bowie. There was loads of Bowie chat – Reeves had some amazing stories. And then we’d all get drunk.”

It’s been a tumultuous several years for The Twilight Sad. Taken under the wing of The Cure, they’ve become one of the big new things in angst-splashed rock. Yet there have been dark days too. Graham and his bandmates are, in particular, still coming to terms with the death last year of friend and touring mate Scott Hutchison of Frightened Rabbit.

Every time they have played since since the death of Hutchison, whose body was found at Queensferry, near Edinburgh, last May, they have made a point of performing a Frightened Rabbit song. They will do so once again supporting The Cure at Dublin’s Malahide Castle this summer. It will possibly be the most-chill inducing moment in the entire evening.

“We were best friends,” says Graham, a lump in his throat. “Over the last few months it’s really hit home just how much we need to keep talking about Scott and his music and what an amazing person he was. We’ve been playing ‘Keep Yourself Warm’ at all our gigs. Just so we can sing Scott’s words every night.

“If there’s someone who comes to one of our gigs and doesn’t know Frightened Rabbit… perhaps they will be introduced. It’s a safe space. A lot of people have not been able to have any release over Scott’s death. I know I’ll never get over it. But I want to remember – I want to remember his music. We’ve got to keep talking about him and his songs.”

The topsy-turvy trajectory has continued with the release of The Twilight Sad’s fifth album, It Won’t Be Like This All The Time. It’s gone Top 20 in the UK and hit number one with a bullet in Scotland. For a downbeat Scottish indie band to be lairds of all they survey, is a novelty not lost on Graham. Yet with many of the songs written in the aftermath of Hutchison’s death, it is a bittersweet victory.

“It’s crazy,” he nods. “We knocked The Greatest Showman off number one in Scotland. That is not a sentence I ever thought I would utter. It’s been mental.”

There’s been a sense for some time that The Twilight Sad, from North Lanarkshire, on the outskirts of Glasgow, were building towards something. Their sound has always been stark, even maudlin. But they have a flair for waxing anthemic. Indeed, there are obvious parallels with Frightened Rabbit, who likewise tapped into the C***play school of heart-baring pop, without sounding as if they were hocking their souls in the process.

This juxtaposition of uplifting and glum – one of pop’s most irresistible contradictions all the way back to Joy Division – comes together rapturously on It Won’t Be Like This All The Time. The tone on standouts such as ‘[10 Good Reasons for Modern Drugs]’ and ‘I/m Not Here [Missing Face]’ is both devastating and wry.

Graham meanwhile etches a direct line to fellow Scottish artists such as the late Hutchison, and also Arab Strap by singing in his own accent – even as guitars and synths couch the bleakness in an arena-friendly comfort blanket.

The record was not straightforward. Halfway through Graham’s songwriting foil and the band’s guitarist/producer, Andrew MacFarlane, announced he was binning all of the material and starting again.

“He said, ‘Don’t panic – I’ve scrapped all the music.’ After The Cure we had decided we really needed to be top-tier. Andy’s take was that we could do better.”

They’re all tremendously proud of the record, of course. Yet when Graham steps back he also takes heart from the fact an old-fashioned rock band are still capable of whipping such enthusiasm among the music-streaming masses.

“The whole HMV declaring bankruptcy thing was another stumbling block. We were keenly aware people wouldn’t be able to get the record at HMV. To know that people are going out to record shops and buying the album – that benefits the whole industry. It’s nice to see people out there supporting independent music.”

It Won’t Be Like This All the Time is out now. The Twilight Sad play with The Cure at Malahide Castle on June 8.