I have noticed on several websites, including this one, that a large number of people who are searching either or both of these individuals (they were brothers and I am descended from William) have listed their parents as William Brereton (3rd baron) and Lady Elizabeth Goring daughter of Earl of Norwich.While it is true that that couple had sons William and Thomas, among other children, they are not the William and Thomas that went to Virginia.
First: Thomas in Virginia was older than William; the opposite was true of William and Elizabeth's sons William and Thomas.
Second: William and Elizabeth's William and Thomas did not go to America, they both died in England.
Third: Of the son William of William and Elizabeth, none of his children had children that survived to adulthood and it is not clear that they ever had any children.
Fourth: The source of my information is the book titled ANCIENTE WHISPERS-A BRIEF HISTORY OF THIRTY-ONE GENERATIONS OF THE BRERETONS, A GREAT LANDED CHESHIRE FAMILY by Anthony Salusbury Brereton, published by Brereton Press, London, copyright 1999, ISBN 0-9534578-0-X, see family tree on page 235.
In that book, the author mentions that several Breretons went to the New World; he does not identify any of them by name.