He was the grandson of barrister Nathaniel Pigott (1661–1737), a Roman Catholic and intimate friend of poet Alexander Pope, who eulogised him in an epitaph inscribed in the parish church of Twickenham.
The younger Nathaniel Pigott married Anna Mathurina, daughter of Monsieur de Bériol, and spent some years at Caen in Normandy for the education of his children.
The Academy of Sciences of Caen chose him a foreign member about 1764, and he observed there, with John Dollond's six-foot achromatic telescope, the partial solar eclipse of 16 August 1765.
His observations of the transit of Venus on 3 June 1769 were transmitted to the French Academy of Sciences; his meteorological record at Caen, from 1765 to 1769, to the Royal Society, of which body he was elected a fellow on 16 January 1772.
The longitudes were obtained from observations of the eclipses of Jupiter's satellites, the latitudes by means of meridian altitudes taken with a Bird's quadrant lent by the Royal Society.