As Paul himself told journalist David Wigg:
"I was just playing the piano in Liverpool, my dad's house, and my sister Ruth's piano book - she was learning piano, and you know those sort of 'D'Ye Ken John Peel' and 'Golden Slumbers' and your old favourites was up on the...thing, y'know, the stand y'know, there was a little book with all those words in it and stuff... so I was just flicking through it, and I came to 'Golden Slumbers' you know, so I just started - coz I can't read music so I didn't know the tune, I can't remember the old tune y'know - so I started just playing my tune to it, and then I liked the words so I just kept that, y'know, then it fitted with another bit of song I had, which was the verse in between it, so I just made that into a song... just happened coz I was reading her book".
So Paul lifted the lyrics but the tune is his - and now I'm intrigued to find out what the original tune was!