They then leave the vehicle to visit the barber's shop mentioned in the song - leaving the owner in sheer disbelief.
Corden, 39, kicked things off by calling the former member of The Beatles, 76, in hopes of finding someone to accompany him in the carpool lane.
During the latest edition of Carpool Karaoke, Corden sheds a few tears as the pair sing Let It Be while touring Sir Paul's home city. "Yeah, I need somebody, not just anybody, please, please help me".
Paul directed James to the road he immortalized in song, Penny Lane, whose famous sign they autographed.
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He was awaiting trial for charges of false imprisonment, witness tampering and battery of the pregnant woman before his death. Last November, Williams was arrested on charges of cocaine possession and possessing a weapon while being a convicted felon.
"So, I wrote the song, 'Let It Be, '" McCartney concluded. What'd she say? Let it be?
As they made their way down the road, the song began to play on the radio and the former Beatle sang along before they left the vehicle and the singer signed his autograph on the road sign.
Corden told him: "Your music is so full of positivity and joy and a message of love and togetherness, I feel like it's more relevant today than it's maybe ever been".
The guys then ended up at a pub where Paul surprised the locals by performing several songs for an emotional crowd.
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Its duties target goods worth $3.3bn (£2.5bn) after the United States imposed tariffs on the bloc's steel and aluminium. European steel producers are concerned about a loss of market access but also that steel from elsewhere will flood in.
He agreed, saying: "We expected it to last 10 years, but it keeps going on, and on, and on".
Corden replied, "That's the most lovely story I've ever heard". Along the way, he discussed the inspirations behind and places where he wrote classic songs, showing Corden the room in which he and John Lennon used to rehearse "She Loves You", and how McCartney's dad thought the chorus should sound less American and they should sing, "She loves you/Yes, yes, yes", instead of the very American "Yeah, yeah, yeah".
The pub-goers are seen putting an array of Beatles hits on the jukebox, before the curtain drops to reveal that McCartney will be playing them live.
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REUTERS/Kevin LamarqueFirst lady Melania Trump boards the plane as she departs Joint Base Andrews on her way to Texas on June 21. Trump made a surprise visit Thursday. " Melania has learned how dishonest they are, and she truly no longer cares! " he tweeted.