From Wikitree: It should be clear to all Randall Family researchers that the immigrant, John Randall of Newport and Westerly, Rhode Island, cannot currently be linked through primary evidence to any Randall Family in England, including the Randalls of Bath.
Disproven: Many generations ago, it was commonly believed that John the Immigrant was the son of Matthew Randall, “Lord Mayor” of the City of Bath, in Somerset England. In more recent times, it was conclusively determined that John could not have been the son of Mayor Matthew, as this son grew up to become the head of the Draper's Guild in London and has been proven to have lived out his entire life in England.[1] [Note, in 1909, Stephen Moorehouse Randall further confused this story when he mistakenly gave John the Draper the birthdate or 1629, rather than 1609, an error which has been repeated it numerous subsequent publications.[2]
https://www.wikitree.com/wiki/Randall-142#DISPUTED_ENGLISH_ORIGINS
In light of these comments, I have detached the parents currently attached to John Randall, I Rev. Matthew Randall and Margaret Randall
