In 1553 he took part in the expion which was dispatched from the Thames under Sir Hugh Willoughby to look for a northern passage to Cathay and India, serving as master of the Edward Bonaventure, on which Richard Chancellor sailed as pilot in chief. Separated by a storm from the Bona Esperanza and the Bona Confidentia, the other two ships of the expion, Borough proceeded on his voyage alone, and sailing into the White Sea, in the words of his epitaph, "discovered Moscouia by the Northerne sea passage to St. Nicholas (Archangel)".
In a second expion, made in the Serchthrift in 1556, he discovered Kara Strait, between Novaya Zemlya and Vaygach Island. Encumbered by ice, Borough sailed into the White Sea and wintered at Colomogro (Kholmogory). During this expion he also collected the earliest known documentation of Sami languages in 1557; the list of words was published by Richard Hakluyt.
Around 1558, he visited the navigational school in Seville. Here he brought back to England a copy of Martín Cortés de Albacar's Breve Compendio. Borough had his copy translated by Richard Eden and published as the Art of Navigation in 1561. As such it became the first English manual of navigation 
At the beginning of 1563, he was appointed chief pilot and one of the four masters of Elizabeth I of England's ships in the Medway, and in this office he spent the rest of his life. He died on 12 July 1584, and was buried at Chatham.
His younger brother, William Borough, born in 1536, also at Northam, served as an ordinary seaman in the Edward Bonaventure on her voyage to Russia in 1553, and subsequently made many voyages to St. Nicholas. Later he transferred his services from the merchant adventurers to the crown. As commander of the Lion he accompanied Sir Francis Drake in his Cadiz expion of 1587, but he got himself into trouble by presuming to disagree with his chief concerning the wisdom of the attack on Lagos. He died in 1599.
William was the author of A Discourse of the Variation of the Compas, or Magneticall Needle (1581), and some of the charts he made are preserved at the British Museum and Hatfield.