[6] He was the younger of the two sons of Lewis III Incledon (1636-1699) of Buckland House, Braunton, about 5 miles to the north-west of Pilton, by his second wife, whom he married at nearby Tawstock, Elizabeth Fane (d.1717), daughter of Hon.

During his first mayoralty of the Borough of Barnstaple (1712–13) he was responsible for supervising the building of the Mercantile Exchange, a grade I listed building now known as Queen Anne's Walk, on Barnstaple Quay, as is recorded on the east parapet of the building by a sculpture of his armorials and a contemporary brass plaque inscribed in Latin as follows: Above is a plumed helm placed on a fasces, part of an antique trophy of arms.

Robert Incledon married twice: He died and was buried on 9 December 1758 in Pilton Church.

He is commemorated twice in Pilton Church: by his own monument and by the depiction of the arms of Incledon impaling Lethbridge, he is commemorated on the "big and sumptuous" mural monument surviving in Pilton Church[9] to his father-in-law Christopher Lethbridge (d.1713) of Westaway House, Pilton.

His mural monument survives in Pilton Church inscribed as follows: And inscribed below: Above are shown the arms of Incledon: Argent, a chevron engrailed between three tuns sable fire issuing from the bung hole proper impaling: Sandford Azure, three bars wavy argent.