Jackie Lomax. (With a backup band consisting of Geroge Harrison, Eric Clapton, Nicky Hopkins, Paul McCartney, and Ringo Starr!)
Oddly enough, on Apple Records, as well. He and Badfinger being the primary Altogether Other acts, aside from that one band and its members. One thing you can say about this single, it was tough to find good session players back then. You just had to make do.
Well, not to slight Doris Troy and others...
The Beatles's demo for the song, remastered: https://www.youtube.com/watch?v=rTzPY_Zwyoc