No. The song was written and recorded by Donovan, who had earlier helped The Beatles with "Yellow Submarine". There were stories that Paul McCartney added the "quite rightly" part in the song, but he didn't. There are also unconfirmed stories that one or more of the Beatles sang in the chorus of "Mellow Yellow".
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The main singers were John Lennon and Paul McCartney in the Beatles.
No, that was the Who, a few years after the Beatles broke up.
No
The Beatles sang Theodorakis in 1963, the title of the soon was "Honeymoon Song"
Yellow Submarine