June 14, 2018 11:59 AM

Even before heading across the pond, James Corden is offering a glimpse of what to expect from his Carpool Karaoke with Sir Paul McCartney, which will air next week during The Late Late Show‘s week of London episodes.

“I’ll never ever forget it,” Corden tells PEOPLE editor-in-chief Jess Cagle during his upcoming episode of The Jess Cagle Interview. “It was the most incredible day I’ve ever had.”

“If it turns out half as good as it felt doing it, I think we may have captured something really special,” Corden adds.

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The host, 39, and the Beatle, 75, will sing their way through a tour of McCartney’s hometown of Liverpool.

“It’s incredible that a genuine icon, a living legend like that would go, ‘Yeah, I’ll come,'” Corden marvels. “We shot with him for like six hours, which is insane.”

When asked what songs made the playlist, Corden revealed one of the must-haves: “‘Drive My Car,’ because it, you know, makes sense.”

This wasn’t the first time Corden and McCartney had met. Several years ago, Corden recruited the musician to participate in a Comic Relief sketch with the promise that he would name his son after him. Sure enough, McCartney came through, and Corden kept his end of the bargain when his son, Max McCartney Corden, was born in March 2011.

  • Watch the full episode of The Jess Cagle Interview: James Corden, streaming now on PeopleTV.com, or download the PeopleTV app on your favorite device.

“I always come through on a promise,” Corden told PEOPLE in a previous interview. “I sent Paul a picture of Max’s birth certificate and he was so lovely about that. He couldn’t believe I went through with it.”

“A week later, the most beautiful cashmere rug arrived,” he added. “And embroidered on the rug it read, ‘To Max, from one McCartney to another. Love, your Uncle Paul.'”

The Late Late Show returns to London to broadcast from Central Hall Westminster June 18-21 at 12:37 a.m. ET/PT on CBS.

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