He was educated at Winchester College and New College, Oxford and succeeded his father as 6th baronet on 12 November 1726. He made his Grand Tour in 1737-40 during which he visited Paris, Geneva, Rome, Florence and Milan. While living in Rome, Lady Mary Wortley Montagu recorded him as having slept with his landlady, with the encouragement of his landlord. In 1742 he was elected to the Society of Dilettanti, a group of gentlemen who wanted to maintain an interest in the antiquarian and artistic pursuits which they had enjoyed abroad. George Knapton, the official portraitist of the society, painted his portrait in 1744, in which he is depicted on board a ship holding a punch bowl inscribed with a line from Horace's Odes: "dulce est desipere in loco". He was elected Member of Parliament for Barnstaple in 1748 and supported the Whigs. In this seat he replaced his first cousin Henry Rolle, 1st Baron Rolle who had been elevated to the House of Lords in 1748. In 1752 he went to Bremen, Hamburg and Lübeck as a delegate for the 'Society for Carrying on the Herring Fishery'. He rebuilt the pier at Ilfracombe, of which manor he was lord, and established better arrangements for English fishermen in Bremen, Hamburg, Lübeck and Copenhagen.
Secondly in 1755 he married Ellen Thresher, a daughter and co-heiress of John Thresher of Bradford on Avon, Wiltshire. She died at her house in The Circus, Bath, Somerset, on 3 December 1813. His children by Ellen were two sons and four daughters:
*Sir Bourchier Wrey, 7th Baronet , eldest son and heir.
*Rev. Bourchier William Wrey, Rector of Tawstock 1801–1839, who re-built as his residence Corffe House within the parish. In 1789 he married Sophia Bethell, daughter of George Bethell. His mural monument survives in Tawstock Church inscribed as follows:
*Ellen Wrey.
*Dyonisia Wrey, wife of Robert Harding and mother of the Devon historian Lt-Col. William Harding of Upcott in the parish of Pilton in North Devon, about 3 miles north of Tawstock.
Sir Bourchier Wrey died 13 April 1784 and was interred in Tawstock church where survives his monument. He was succeeded by his eldest son Sir Bourchier Wrey, 7th Baronet.
Monument at Tawstock
A monument to Sir Bourchier Wrey, 6th Baronet, described by Pevsner as "stately", exists in the south transept of Tawstock Church, being a plain free-standing urn on a big square pedestal, railed off by iron railings. The north side of the base is inscribed as follows: The east side is inscribed:
