I didn’t know about this particular coincidence until I bought a little ripper of a book, The Beatles: The Complete Guide To Their Music.
(There’s a whole series of “The Complete Guide To Their Music” books, and a few of them are currently available online for $4.99 at The Music Shop. I bought that one and the one about ABBA. I can’t speak for the others in the series, but The Beatles book packs a heap of information about their songs into a couple of hundred pages.)
In the entry for “Lady Madonna“, the guide mentions that the piano intro was “lifted almost directly from Humphrey Lyttelton‘s mid-Fifties British jazz classic, ‘Bad Penny Blues‘”. I’d never heard “Bad Penny Blues” (or even heard of it), so I hunted it down and had a listen.