From 1609 a William Barret worked in partnership with Edward Blount, the printer of The First Folio of the works of Shakespeare in 1623. Given that the link is purely speculative, the fact that he was a printer or bookbinder might connect him to our Barratt line.
It seems that the same William Barret might have worked with or for another printer of Shakespeare’s work, William Stansby, from 1608 to 1624. He is listed in this context as a bookseller. There is record of Montaigne, Michel de, 1533–1592. [Essais. English] Essays vvritten in French done into English, according to the last French edition, by Iohn Florio.... London: Printed by Melch. Bradvvood for Edvvard Blount and William Barret, 1613.
This indicates that William Barret was a bookseller. Other records indicate that he was a stationer between 1605 and 1620. At that time, ‘stationer’ meant a trader with a fixed address, often selling books, as opposed to an itinerant bookseller.
The Cambridge History of English and American Literature reports of Edward Blount:
From 1609, he was, for a time, in partnership with William Barret, and together they issued, in 1612, Shelton’s translation of the first part of Don Quixote, notable as being the first translation of Cervantes’s great novel into any language. In 1622, he brought out James Mabbe’s rendering of Aleman’s The Rogue, or the life of Guzman de Alfarache; and to Earle’s Microcosmographie, which he published anonymously in 1628, he wrote a preface.