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Plant and two of the band gather round a microphone to supply harmonies as Krauss sings Down to the River to Pray, one of the songs she sang on another Burnett production, the eight-million-selling soundtrack to the Coen brothers film O Brother, Where Art Thou? “Do we need to get in tight?” Plant asks Burnett. “Like the Beverly Sisters?” Then, switching from goofball to rock icon, Plant leads the band and Krauss through a version of The Battle Of Evermore, from Led Zeppelin IV – the classic album that has sold 23 million copies in America alone.

“It’s found its own place,” Plant offers by way of explanation of Raising Sand. “We didn’t expect any kind of interest outside a particular area – and it’s really quite remarkable how people just picked up on it.”

Indeed, the album has already entered the ether of American mainstream culture, partly because of a new advertising campaign for the chain store JC Penney that premiered during this year’s Oscars ceremony. It uses the album’s Killing the Blues, a song written by Chris Isaak’s guitarist, Roly Salley. “The ad is heavy on sentiment,” said the press release for the commercial, which features images of “heartland” Americana – family reunions, Fourth of July celebrations. “Now I am guilty of something I hope you never do,” Plant and Krauss’s enmeshed voices sing, “because there is nothing sadder than losing yourself in love… Somebody said they saw me swinging the world by the tail…”

“When I first heard that song, after T. Bone sent his collection of songs, I was driving through the Welsh borders in Herefordshire,” says Plant, who splits his time between homes in Worcestershire and Primrose Hill, North London. “I just stopped the car. It was so poignant, so masterly.”

“And the melody was so sweet,” adds Krauss, who lives in Nashville with her eight-year-old son. “When you combine a melody that lifts you up with a lyric like that, it’s a twisted thing. When you get that combination, that is really something.”

Last night this hilariously unlikely but strangely like-minded pair attended the Country Music Television awards in Nashville. The ceremony was hosted by Hannah Montana, aka Miley Cyrus, the biggest teenage star in America and daughter of Nineties country sensation Billy Ray Cyrus. They won an award for their video for Gone Gone Gone, beating the Eagles and Willie Nelson. It’s all a long way from Stairway to Heaven. As Plant declares with evident delight during our interview: “What a place for me to land up. I’m nearly 60 years old. Look,” he says, waggling his feet, “I’ve got new cowboy boots and these flares are great – they’re a 33-inch waist and they’re ladies’ jeans.”

We are in the Germantown area of Nashville, in the remodelled environs of an old meatpacking plant. Old Meatpacking Plant – still trim and still blessed with locks that look like the Cowardly Lion’s after his makeover in Oz – fidgets around on the sofa next to the seemingly demure, heavily made-up Krauss, who is resplendent in dungarees and a nice pink sweater. She cackles: “Those are ladies’ jeans?”

“Yeah. They’re from, what’s it called, Lucky. The guy said to me, ‘Hey man, you wanna have some of them jeans like you used to wear in ’71.’”

I suggest that with the jeans he used to wear in ’71, everyone could see his willy.

“Oh, I haven’t got one of them now!”

Plant chuckles. “I had to take if off for this project. I had to get rid of all that. I’m learning how to eat corn on the cob with no teeth.”

Krauss, initially failing to grasp what a willy is, says: “I wasn’t sure what you meant there. Now I got it!”

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