I have traced my Hawthorn family to Bray, Berkshire Co., England (Robert Hawthorn, born @ 1605). My theory, though unproven, is that the family was among those who moved from Catholicism to Anglicanism to Puritanism to Separatism to Baptist. I believe the English spelling was actually "Hathorn" or "Hathorne." Major William Hathorn was among the Puritans who formed the Massachusetts Bay Company and arrived in New England with John Winthrop ("Directory of the Ancestral Heads of New England Families 1620-1700"). My direct line does not seem to be among those Puritans, however, but probably among Baptists who migrated from England to Virginia sometime between 1665 and 1705. Many Protestants left England during those years because of the "Test Act" which followed Cromwell's removal and Charles II's return from exile. Baptists along with other non-conformists were "precluded from naval, military, civil, and municipal services" (Robert G. Torbet, "A History of Baptists").
I tell you all of this to say that I believe the Ha(w)thorn family became Separatist and then Protestant, and during those years of persecution, particularly Bloody Mary's reign (1553-1558), they scattered. A group of Protestants went from England to Europe, and possibly met up with the Anabaptists (Dutch Mennonites). Therefore, you may find information by researching your family's religious background. I do know that church records exist in Berkshire County, England, (and later in Surry County, Virginia) until the family renounced infant baptism.