Sir Arthur Bassett (1541–1586) was a member of the prominent west-country Basset family and was MP for Barnstaple in 1563 and Devon in 1572. He served as JP for Devon from 1569 to his death and as Sheriff of Devon in 1574–5. He was knighted in 1575. He had been appointed deputy warden of Stannaries by 1580.
He was the eldest son of John Bassett (died 1541) (son of Sir John Bassett (died 1529)) of Heanton Punchardon and Umberleigh in Devon and Tehidy in Cornwall, Sheriff of Cornwall in 1518 and 1523, by his wife Frances Plantagenet, the daughter and co-heiress of his step-father Arthur Plantagenet, 1st Viscount Lisle, bastard son of King Edward IV. Arthur Bassett was thus a grandson of Arthur Plantagenet on his mother's side, and on his father's side a grandson of Honor Plantagenet, Viscountess Lisle, née Honor Grenville, the second wife of Sir John Bassett (died 1529) who married secondly as his second wife the aforementioned Arthur Plantagenet. Making Bassett the cousin of Sir Richard Grenville the Younger, via Grenville's Aunt, Honor Grenville.
Bassett was by religion a puritan, and a friend of the powerful Francis Russell, 2nd Earl of Bedford (1527–1585), of whose will he was an overseer. He helped to finance the expedition to the South Seas undertaken by his cousin, Sir Richard Grenville. His father-in-law Sir John Chichester (died 1569) conveyed to him for a term of five years the rectory of Pilton Priory, which he had himself acquired following the Dissolution of the Monasteries. He volunteered for military service in the Netherlands to defend the Protestant cause against the Spanish, where in 1586 he obtained a command at The Hague, serving under Robert Dudley, 1st Earl of Leicester, the maternal uncle of his friend Sir Philip Sidney who was killed in 1586 at the Battle of Zutphen.