“I’m a Guardian subscriber!”

Oh, come now, Steve, you’re just buttering me up.

“I love the arts coverage!”

It’s not every day you get sweet-talked by a comedy legend; one of “the funniest, most influential and much-loved talents of the past century”, indeed. That’s how Steve Martin and Martin Short are described – much to their embarrassment – in the publicity for their UK comedy tour, announced on Monday. I’ve got them both on the phone from Dallas, Texas, on the morning of their latest gig, to discuss this late-career double act and UK visit. From 5,000 miles away, they hype up the Guardian, banter and backchat, punctuated by incongruous blasts on the banjo from Martin, aka one-sixth of bluegrass band Steep Canyon Rangers, who tour with the show.

The pair have been close friends since co-starring in The Three Amigos (with Chevy Chase) in 1986. “We’ve been through a lot together,” says Martin: “Marriage, deaths, births and divorces.” It was shortly after the death of Short’s wife, Nancy Dolman, and before the birth of Martin’s first child (he was 67 at the time), that they were asked to interview one another on stage at the Chicago comedy festival. “It went really well,” says Martin, “and we said, ‘Let’s do it again, that was fun.’ And the more we did it, the more we thought, ‘We need a real show, we can’t just sit there and talk.’”

So they came up with one, then were Emmy-nominated for its Netflix incarnation, entitled An Evening You Will Forget for the Rest of Your Life. The actor (and Short’s pal) Catherine O’Hara described it as “a children’s show for adults”, while others reached for the term vaudeville – which mystifies Martin and Short. “I’ve never quite understood what vaudeville means,” says the latter, “except that it’s a quick succession of different acts. Which describes our show, I guess – because Steve and I do stuff together, then I do stuff alone, then Steve does, then he plays the banjo and we have this brilliant band come on.” The term also reflects the old-school nature of the pair’s relationship: their quick back-and-forth, the playful spirit of one-upmanship, the teasing that doesn’t even pretend to conceal their fond camaraderie.

Facebook Twitter Pinterest ‘We’ve been through a lot together’ … Steve Martin, Martin Short and Chevy Chase in Three Amigos! Photograph: Allstar/Orion Pictures

“We’re absolutely a double act,” says Short. Martin references Dean Martin and Jerry Lewis, Abbott and Costello – but insists: “We don’t rely on nostalgia in our show.” They’re not trying to be old-fashioned, nor cash in on affection for their movie work. Yes, admits Short: “If you’ve been in the movies when someone was 12 or 13, and now they’re 40 and seeing your show, there’s a nice feeling to that. It feels like you’ve been part of their life.” But the duo aren’t resting on laurels, says Martin. “I like to think of this as hopefully among the funniest shows the audience has ever seen. That’s what we’re trying to create.”

Cue another blast of banjo, twanging down the line from Dallas. Time was, Martin was the hottest property in world comedy, a multi-award-winning standup (#11 of all time in Rolling Stone’s 2017 roundup) with Hollywood at his feet. Then, in 1981, he quit, “essentially depressed”, he later said, and out of ideas. It was banjo-playing that lured him back on stage – but this matchup with Short (a fellow 80s-era Saturday Night Live star, if not an exact contemporary) represents a return to live comedy after three decades away. “And I’m really enjoying it because of the company,” he says. “I’ve done things on my own, and it’s not the same as having friends to share the ups and downs with. Although there are very few downs, I must say.” Short agrees: “We absolutely adore doing this show.” That’s why they’re hitting the road at an age (Short is 69, Martin 74) when – in Short’s own modest appraisal – “we’ve got the rent covered.”

“That’s easy for you to say, Marty!” pipes up Martin.

“Well, I have the rent covered,” says Short. “He buys expensive paintings.”

Facebook Twitter Pinterest Twang! Steve Martin on stage in 2011. Photograph: Angela Weiss/WireImage

Do they feel connected with the 21st-century comedy scene? At this question, discord breaks out. “I feel like we’re pretty connected,” says Short – but Martin interrupts. “I was just going to disagree. I have no idea what’s going on.” Turns out, Martin retains a post-traumatic dislike of live comedy clubs. “I get this taste of cheap wine in my mouth and hostile audiences. So I don’t like to go see comedy live.” But if you want to be the funniest show ever, don’t you need to keep up with the competition? “Well, I don’t feel like we’re in competition,” says Martin. “I used to.”

That’s why both are happy that their double act has assembled only in the twilight of their careers. “It’s the perfect time,” they both say. “If we’d done it in the 80s,” says Martin, “we would measure it a little more and be more competitive. But at this point we’re not. We’re just playing to an audience. We like them, they like us, and everything is fine.” Both agree that Martin is the “sensitive” one of the duo, more concerned about audience reaction. “You’re more of an artist,” says Short – whereas he, Short, is the “confident” one. “We always say about Marty that he’s laughing on the outside,” says Martin, “and laughing on the inside too.”

How a British audience will react to their show – entitled The Funniest Show in Town at the Moment, and “70% different” (says Martin) to the Netflix special – is “an unknown question”. So too the one with which Martin signs off from our call: “Do you think the Queen will come to our show?” In London, they’re playing the Royal Albert Hall, and “we can get her comps,” says Short, faux-eagerly. Might the Queen be a Three Amigos fan? You wouldn’t bet against it. “I know Americans can’t get knighthoods,” says Martin. “But they always make exceptions! I’m going to be sitting by the phone waiting for my knighthood call.”