Dave Carter wrote:
"Davy Jones was English. He was from Manchester. Should he have sung in a Manchester accent? What is such an accent anyway? One you hear on Coronation Street? Davy Jones did in fact begin his career in Coronation Street."

A little know fact. Davy was Ena Sharles grandson. and I'm pretty sure I can detect traces of Ena's accent in Davy's delivery of "Daydream Believer".

But, being serious, Davy was, first and foremost, an actor, and in The Monkees he's playing the part of a Englishman in an American pop band and so the accent he used was probably created - to a large extent - for the part.