Rachel Herrmann published a great article about this a few years ago in William and Mary Quarterly - you can find it here. She argues that while "historians generally take the case of cannibalism in Jamestown for granted" in fact "the existence of cannibalism in Virginia is not easily verifiable." While Herrmann acknowledges accounts like John Smith's:

so great was our famine, that a Salvage we slew, and buried, the poorer sort tooke him up againe and eat him, and so did divers one another boyled and stewed with roots and herbs: And one amongst the rest did kill his wife, powdered her, and had eaten part of her before it was knowne, for which hee was executed, as hee well deserved; now whether shee was better roasted, boyled or carbonado’d, I know not, but of such a dish as powdered wife I never heard of

Herrmann argues that:

Cannibalism may or may not have taken place during 1609–10; some evidence exists to suggest that it did, whereas other accounts might be cited to argue that it did not. Ultimately, there is no way to answer this particular question definitively... What historians can do is consider the various accounts together and acknowledge that cannibalism should no longer be stated as a bare fact in the chronology of early Jamestown.

The kicker here is that 2 years after Herrmann published, archeologists announced that they had uncovered physical evidence of cannibalism: the remains of a young girl (about age 14), who had very clearly been dismembered, and whose bones were found in a heap of bones from dogs, cats, and horses that had also been consumed during the starving time:

“The chops to the forehead are very tentative, very incomplete,” says Douglas Owsley, the Smithsonian forensic anthropologist who analyzed the bones after they were found by archaeologists from Preservation Virginia. “Then, the body was turned over, and there were four strikes to the back of the head, one of which was the strongest and split the skull in half. A penetrating wound was then made to the left temple, probably by a single-sided knife, which was used to pry open the head and remove the brain.”

[...]

Lead archaeologist William Kelso today at a press conference at the National Museum of Natural History, we now have the first direct evidence of cannibalism at Jamestown, the oldest permanent English colony in the Americas. “Historians have gone back and forth on whether this sort of thing really happened there,” Owsley says. “Given these bones in a trash pit, all cut and chopped up, it's clear that this body was dismembered for consumption.”

source

The archeological evidence is pretty conclusive, and it's confirmation that settlers were desperate enough to eat other people (along with dogs, cats, horses, etc). But there's no real evidence how widespread it was.