He was the eldest son and heir of Sir Arthur Bassett, 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, a daughter of Sir John Chichester, MP, lord of the manor of Raleigh in the parish of Pilton, Devon.
Due to his Plantagenet ancestry he made what turned out to be a foolish and costly decision to offer himself as one of the many claimants to the throne of England after the death of Queen Elizabeth, perhaps encouraged by his father-in-law Peryam. He suffered a heavy fine for his action which according to the biographer John Prince, involved the sale of thirty of the family's manors.
Marriage and children
He married Elizabeth Periam the second daughter and co-heiress of Sir William Peryam, of Little Fulford, near Crediton in Devon, Lord Chief Baron of the Exchequer. Her mural monument survives in the Basset Chapel of Heanton Punchardon Church. Within a lozenge at the top and on an escutcheon to the sinister are shown her paternal arms of Peryam: Gules, a chevron engrailed or between three lion's faces affrontes of the last. The arms of Peryam are also shown on an oval cartouche underneath, impaled by Bassett.
Sons
Arthur Basset, eldest son and heir, who died childless. In 1635 he erected the surviving monument to his mother in Heanton Punchardon Church, as is recorded by part of the inscription as follows: "Arthur Bassett, Esquire, her sorrowing first-born son, of a duty of gratitude and respect therefore placed this monument to his mother in the year of Our Lord 1635".
Col. Arthur Basset, second son and heir to his elder brother. He was a law student at the Inner Temple in 1616 and during the Civil War served as a Royalist commander. For his delinquency he was fined by Parliament and compounded for his estates in the sum of £1,321 6 shillings 6 pence. He served as Deputy Lieutenant of Devon. He married Agnes Leigh, daughter of Sir William Leigh of Northam, Devon. His elaborate mural monument survives in Heanton Punchardon Church.
William Basset, third son, whose monument survives in Atherington Church, the parish church of Umberleigh
Elizabeth Basset, second daughter, who in 1621 married George Yeo, lord of the manor of Huish, Devon, who was admitted to the Inner Temple in 1618. Her descendant continued at Huish until the death unmarried in 1782 of the last in the male line, Edward Roe Yeo, twice MP for Coventry.
Elinor Basset, third daughter, who died unmarried in 1634/5.
Mary Basset, fourth daughter, who in 1631 married Jonathan Sparke of Plymouth, who was the second son of John Sparke of The Friary, in the parish of St Jude, Plymouth, Devon, Member of Parliament for Mitchell. Jonathan Sparke's mother was Deborah Rashleigh, a daughter of John Rashleigh, of Menabilly, a cousin of Mary Basset. Mary's eldest son was Sir John Sparke, MP, of the Friary, Plymouth, who is mentioned in the Travel Journal of Cosimo III de' Medici, Grand Duke of Tuscany who was visiting Plymouth on 5 April 1669:
Death and burial
He died on 11 November 1641 aged 68 and was buried in the Basset Chapel of Umberleigh Church, in the floor of which survives his plain ledger stone inscribed in Latin as follows:
