Sir Robert Basset (1573-1641), lord of the manor of Umberleigh and lord of the manor of Heanton Punchardon in Devon, England, was MP for Plymouth in 1593.
He was the eldest son and heir of Sir Arthur Bassett (1541-1586), of Umberleigh and Heanton Punchardon, a member of the ancient and prominent west-country Basset family, MP for Barnstaple in 1563 and Devon in 1572 and Sheriff of Devon in 1574-5. Robert's mother was Eleanor Chichester (died 1585), a daughter of Sir John Chichester (died 1569), MP, lord of the manor of Raleigh in the parish of Pilton, Devon.
His grandfather John Basset (1518–1541) had married Frances Plantagenet, the daughter and co-heiress of his step-father Arthur Plantagenet, 1st Viscount Lisle (died 1542), bastard son of King Edward IV. Sir Robert Basset was thus a great-grandson of Arthur Plantagenet, 1st Viscount Lisle on his paternal grandmother's side. On his paternal grtandfather's side Robert Basset was a great-grandson of Honor Plantagenet, Viscountess Lisle (c.1493/5–1566), née Honor Grenville (the second wife of Sir John Basset (1462–1528) of Umberleigh) who married secondly (as his second wife) the aforementioned Arthur Plantagenet.