"Blue-Eyed Soul"
It's enough that the roots of rock music were mainly in the early works of black artists -- the blues musicians and the R&B vocal groups. But later (especially in the 60's) some white artists went so far as to actually imitate black pronunciation. It wasn't necessary -- but it wasn't bad either.
The Rolling Stones did it all the time, of course; the Beatles did it now and then. Other British bands that sang black included the Animals ("The House of the Rising Sun") and Procol Harum ("A Whiter Shade of Pale"). But for the ultimate British white-soul sound, try this:
The Spencer Davis Group: "Gimme Some Loving"
https://www.youtube.com/watch?v=x3kZEjD3Gr8
In America, I guess the best-ever white soul sound was that of the Righteous Brothers ("You've Lost That Lovin' Feeling"). Another act that attempted the same thing, though with less commercial success, was
The Walker Brothers: "The Sun Ain't Gonna Shine Any More"
https://www.youtube.com/watch?v=Q11ium_-Lv8
Then came the 60's "punk rock" or "garage rock" explosion, and with it came a lot of white bands that sang black. Here's one that was actually a song ABOUT racism:
The Standells: "Sometimes Good Guys Don't Wear White"
https://www.youtube.com/watch?v=SIPTDm1YZMQ
And other topical or social-consciousness songs:
The Rascals: "People Got to Be Free"
https://www.youtube.com/watch?v=xYYQx9K6Cb0
The Music Machine: "Talk Talk"
https://www.youtube.com/watch?v=Hvtn-h9eo5g
And many were just love songs or fun songs. Some of these groups only existed briefly, and most people never got to see them; there were some fans who didn't even realize that these groups were white:
The Music Explosion: "Little Bit of Soul"
https://www.youtube.com/watch?v=JxmTYrT2ZMk
The Box Tops: "The Letter"
https://www.youtube.com/watch?v=PKbaj4FB-Iw
Question Mark and the Mysterians: "96 Tears"
https://www.youtube.com/watch?v=Kwr30amfFIs
The Rare Breed: "Beg, Borrow and Steal"
https://www.youtube.com/watch?v=ldVGtqxeGuM
The Syndicate of Sound: "Little Girl"
https://www.youtube.com/watch?v=Dk4kffQoG7w
The Shadows of Knight: "Oh Yeah"
https://www.youtube.com/watch?v=YRuG7M9bA0w
The Soul Survivors: "Expressway to Your Heart"
https://www.youtube.com/watch?v=XX052B1oXdU
And here's one that's really outrageous. I don't even KNOW if this group was white, but I just assume it MUST have been.
006: "Like What, Me Worry?"
https://www.youtube.com/watch?v=cgE6fUUW1vM
Then, of course, there was THIS huge hit back in 1961. Half the kids in my neighborhood didn't know the Dovells were white, and if you told them, they didn't care.
The Dovells: "The Bristol Stomp"
https://www.youtube.com/watch?v=jkmEA3AWock
And finally, here's a pretty ballad from 1967 that was another of those innumerable "one-hit wonders." I didn't find out that the Casinos were white until years later.
The Casinos: "Then You Can Tell Me Goodbye"
https://www.youtube.com/watch?v=zcqOmm-g6w4
And BTW, do BLACK singers ever imitate WHITE pronunciation?
Maybe not, but Tony Williams of the Platters came pretty close to it. In those days it was still common (though not mandatory) for professional pop singers to take "singing lessons" that included speech practice. Maybe that's why Tony's pronunciation was so "perfect" that it sounded a bit artificial.
The Platters: "Twilight Time"
https://www.youtube.com/watch?v=jLM19DWofXc