In the early 70s, Alice Cooper helmed his own secret late-night drinking club. Based in an exclusive loft at Hollywood’s legendary Rainbow Bar and Grill, it provided boozy sanctuary to many fellow stars including Ringo Starr, John Belushi, John Lennon, Keith Moon, Keith Emerson, Harry Nilsson and Marc Bolan. Their all-night drinking sessions took place away from the prying eyes of the media and nagging managers. The staff at the Rainbow dubbed the crew the Hollywood Vampires.

“Because they only saw us at night and all we did was drink!” Cooper laughs down the line from New York. “I remember it, but the lines are a little blurred. Our lines would all get blurred quite a lot. It just seemed to be the place where everybody ended up.”

These days Cooper is plainly doing a lot better than most of his friends, many now departed. A wiry and energetic 70-year-old, he is currently on tour – he’s almost always on tour, but this time it’s with the band he named after the drinking club, formed in 2015 with guitarists Joe Perry (of Aerosmith) and, more intriguingly, Johnny Depp.

The roots of this all-star project stretch back to an intimate gig Cooper played at London’s 100 Club in 2011. Both Cooper and Depp were in the city to film Tim Burton’s horror comedy Dark Shadows. Cooper invited the actor to play a few songs and started toying with the idea of forming a covers band to pay tribute to his fallen drinking buddies. Depp and Perry (whom Cooper has known for decades) joined and the band made their live debut at LA’s Roxy Theatre in September 2015. They released their self-titled debut album the same month, featuring three originals among the classic rock covers. Well-received by rock bibles Kerrang! and Rolling Stone, the Vampires were credited with avoiding self-indulgence – though in the age of #MeToo, it remains to be seen whether they’ll pull off another tribute to macho rock-star excess.

This month they are packing out Europe’s arenas and working on a second album of entirely original material. Quite how this works with three major stars sharing the spotlight is anyone’s guess, though it sounds as though their egos have found an odd equilibrium. “When we put three alpha males in the band, I did think, ‘Oh man, this could be tough,’” Cooper says. “But there’s never been an argument.”

“You’ve got have ego to do what we do,” says Perry, “but with this I’m in a totally different headspace. I can just sit in the corner! It’s fucking great. And Johnny is the real deal, let me tell you.”

Depp’s passion for music is well known. In the early 90s he was a member of the (largely unlistenable) alt-rock supergroup P, alongside Flea of Red Hot Chili Peppers and Gibby Haynes of Butthole Surfers. In 1997 he played slide guitar on Oasis’s Be Here Now and he has performed with everyone from Marilyn Manson to Shane MacGowan.

Allegations of domestic abuse towards ex-wife Amber Heard have affected his career, which was already struggling in the wake of flops like The Lone Ranger and Transcendence. (After Heard accused him of physical and verbal abuse “during the entirety” of their relationship, the couple divorced. Heard received a $7m settlement, which she donated to charity, and the couple released a joint statement describing their relationship as “volatile, but always bound by love”.)

Meanwhile, recent photos of Depp looking gaunt have prompted speculation that he is unwell. Having been told firmly that questions along these lines will bring the interview to a halt, I ask instead what he gets from rock’n’roll. “My day job is a completely different animal, I suppose,” he says. “What do I get from this that I normally don’t get? I get me!” He laughs. “But when I’m up there on stage with these guys, it’s that feeling I had as a kid. It’s freedom. In movies someone is always telling you what to do, but here I have the freedom that my day job doesn’t allow. Most important, it’s really fucking fun.”

Perry is particularly eager to sing Depp’s praises, noting that he first realised that Depp had a talent when he saw him playing acoustic guitar in Lasse Hallström’s 2001 film Chocolat. “Quite often when you watch a movie and someone is playing, you can really tell that it’s not for real,” Perry states. “But he was playing some really cool shit, things I’d never touched on as a guitarist. A lot of actors and actresses have walked our way over the years” – pun presumably intended – “but with Johnny it’s different. There’s a laser focus in his eyes.”

“He trades licks with Joe and I’d put him up against any second guitarist out there,” agrees Cooper, with somewhat faint praise. “He needs to prove himself every night and that’s a good thing. It gives him that edge.”

Hollywood Vampires’ summer tour ends on 8 July in Rome, after which Cooper and Depp will continue working on their second album. Time will tell as to whether their novelty value will survive, but both are adamant that they’re now taking what was once a bit of fun a lot more seriously.

“I think we really found our sound this time; I think we just had it by the tail on the first record,” says Depp. Cooper adds: “We’re doing what we keep telling young bands to do: don’t lose the anger in rock’n’roll, don’t lose that edge, don’t mellow out! All of the songs that have been written so far are really raucous rock’n’roll songs. It’s got a lot of attitude to it.”

Given how many of the original Hollywood Vampires drinking club members are gone, Cooper ranks as one of the great survivors of rock’s first golden era. Perry too, a former addict, has every reason to be thankful. But only last month, reports emerged of a drunk Depp threatening to attack a crew member on a film set. Could this totem to excess, in some perverse way, be a form of rehabilitation?

“What separates survivors from the guys that die?” Depp wonders aloud. “It’s just about having the right people around you, people who care about you, at the right time, to save you from yourself. It’s not a good thing to face on your own,” he says, of alcoholism and addiction, “but some people do. Really, it’s just luck.”

“That is definitely true,” Cooper agrees. “There were times when I should’ve been gone. I’m 70 now and I’m in better shape than I was at 28. At 28 I was a wreck. I’d never heard the word tofu in my life. I was trying to live that lifestyle as fast as I could and it was non-stop.”

Still, he can’t help romanticising the myth of the male rock star. “You just wrote your songs, ate what you could, drank as much as you can and went off to be a great rock band after…. And we looked good doing it!”

• Hollywood Vampires are on tour in the UK (16 June: Birmingham Genting Arena, 17: Manchester Arena, 19: Glasgow SSE Hydro, 20: London SSE Arena)