McCartney told how a dream, in which his mother told him to "let it be", inspired the song of the same name.
Eventually, they end up at a pub to give the locals "the surprise of their life", Corden said.
"I can remember my granddad, who's a musician, and my dad sitting me down and saying, "We're gonna play you the best song that you've ever heard" and I remember them playing me that", Corden explained.
"I didn't feel it coming, it's too much for me". They also stopped by the barber shop mentioned in "Penny Lane" and mingled with excited fans along the sidewalks.
In a break with Carpool Karaoke tradition, the veteran singer then took the wheel and drove Corden - who appeared visibly starstruck - around the streets of Liverpool.
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Published by Beyonce's YouTube channel, the track's artist is listed as The Carters - the couple's family name. The singer delighted fans by dropping a clip from a music video for one of her new tracks on her Instagram .
As they look around, Sir Paul says one of the downstairs rooms is where "me and John would often come to rehearse or to write".
He played A Hard Day's Night, Love Me Do, Back In The USSR and Hey Jude as members of the audience cried.
'I think if my grandad was here now he'd get an absolute kick out of this'.
Shocking the homeowner with an impromptu visit, McCartney shows Corden around the house.
Carpool Karaoke was clearly Corden's breakout, but I like how he's used the segment not as a senseless gag to boost YouTube views, but as a real opportunity to get to know the guests that ride around in the vehicle.
He agreed, saying: "We expected it to last 10 years, but it keeps going on, and on, and on".