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Full disclosure: there may not be a better way of dealing with the post-Glastonbury blues than a lakeside sauna in the land of the midnight sun (that’s Finland) with one of the headline-grabbing acts sitting comfortably (that is, semi-naked) next to you.

Thanks, then, to Brandon Flowers for inviting me, three days after The Killers’ surprise appearance at Worthy Farm, to process the comedown by hopping aboard their private jet and joining the Las Vegas band on tour in northern Europe.

Still, I’d suggest this afternoon’s countryside excursion — a few hours before the foursome headline the Provinssi festival in the small town of Seinäjoki — isn’t an entirely selfless act. Flowers has his own collywobbles to address.

His “internal clock” of worry, the singer reports, was ticking loudly pre-Glastonbury: “Then there was a sigh of relief. Then it started up again for Hyde Park. So that’s where I am right now,” he says, grinning. “I’m not putting down Finland or Sweden or Serbia, but London is constantly at the back of my mind.”

Specifically, this most ambitious, particular and questioning of frontmen is considering the set list for this weekend’s gig. The Killers are now four studio albums in (and a B-sides collection, and a greatest hits) and have crowd-pleasing anthems to spare: Mr Brightside, Jenny Was a Friend of Mine, All These Things That I’ve Done, Human.

But their new album, Wonderful Wonderful, is out in late September. And Flowers — teetotal, diet-conscious, beach body-ready and arbiter of every professional live photograph taken at Killers shows — is pondering how many unreleased songs to play at Hyde Park, which was the first British Summer Time concert to sell out. Will the 65,000 fans want to hear the song co-written with Adele hitmaker Ryan Tedder? The one on which Flowers, to his wide-eyed wonder, shares credits with Brian Eno (and on which the 36-year-old’s three young sons provide backing vocals)? Or should The Killers just roll out The Man, the disco-tastic comeback single, in the video for which Flowers has never looked more buff?

“And if we do play The Man, do we open with it?” he says with a frown. It’s tough to sing, he adds. The vocals were spontaneous, and he didn’t think about the key. “Now I’m realising that I have to do it every night — and it’s high! I got to figure out how to do it.”

The single’s dancefloor-friendly sound was abetted by producer Jacknife Lee. He’s the California-residing Irishman who has worked with everyone from U2 and Snow Patrol to Taylor Swift and Neil Diamond. How did The Killers come to work with him? Flowers squirms.

“It’s impossible to explain this without name-dropping, but Bono suggested it. And it gets worse — I was at this house he was renting in Malibu,” he admits, emitting another yuk-yuk laugh. Facing something of a creative crisis of confidence, he had sought the counsel of one of the rock stars the teenage Mormon kid from smalltown Nevada had idolised. “I was seeking out the ‘Bono talk’,” he says, referring to the wisdom the U2 frontman is known to bestow upon music’s young shavers. “I’d emailed him a couple of times and he could tell that I needed a little help and invited me to visit.”

The stakes are especially high this weekend. London means a lot to Flowers and bandmates Ronnie Vannucci Jr (drums), Dave Keuning (guitar) and Mark Stoermer (bass). In summer 2003 The Killers were a new American band going nowhere at home. But in August that year, Radio 1’s Zane Lowe played their debut single Mr Brightside. The response was feverish.

The following month the band came to London to play four tiny pub/club shows, at Camden’s The Monarch, Dublin Castle and Barfly, and the now-closed Metro on Oxford Street.

'We took this indie deal in the UK. This was our last-ditch effort, and the first time any of us had left the US. And it was magical'

“We were so excited,” says Flowers, smiling his toothy smile. “We had been turned down by every major label in America. So we took this indie deal in the UK. This was our last-ditch effort, and the first time any of us had left the US. And it was magical.”

In rock ’n’ roll terms, “we did the whole thing”. The Killers stayed at The Columbia in Bayswater, the indie band accommodation of choice, “and it was in full swing. There might be a Libertine or a Stroke or a King of Leon in the bar.”

Ushered into a gig by cult British electronic act Ladytron, Flowers heard someone speaking behind him. “You could have blindfolded me and I’d still have known who it was: Neil Tennant,” he says. “I just stared at him. This was the greatest week of my life!”

Fast-forward a decade and The Killers played their most recent London gig: in front of 90,000 fans at Wembley. In a masterstroke, the band marked the June 2013 show by performing a specially composed tune, Wembley Song. With crowd-pleasing diligence Flowers’s lyrics referenced some of the stadium’s greatest hits: World Cup 1966, the “day-oh!” of Freddie Mercury.

“It was hard to treat it like just another show, and I really wanted to make it count. The only thing I could think of was to do the song. And that solidified the experience. It’s a souvenir from it, for people and for us. It’s better than a T-shirt.”

Wembley was a victory lap near the end of the touring cycle for their last studio album, 2012’s Battle Born. Which begs the question: why frontload a campaign for the as-yet-unreleased Wonderful Wonderful with Hyde Park? “I know. We hadn’t even finished recording when we booked it. We didn’t have even The Man or any first single. I remember thinking, ‘We haven’t been over to the UK, we haven’t got an album coming — what are we doing?’ But we agreed to it. And it sold so well the first day, I remember being baffled by it — I couldn’t believe it,” Flowers says.

“But that felt so good, and maybe gave me confidence in the studio. It made me want to wrap up the record. Hyde Park gave us something to shoot for.”

The Killers play Barclaycard Presents British Summer Time Hyde Park on Saturday (bst-hydepark.com)