He was born in London, and was baptised 15 October 1759, the younger son of William Tomkins (1730?–1792), a landscape-painter, and his wife Susanna Callard. Charles Tomkins the antiquarian draughtsman and aquatint engraver was his elder brother.
He became a pupil of Francesco Bartolozzi, and working in the dot and stipple style. Tomkins was engaged as drawing-master to the daughters of George III, and spent time at court, receiving the appointment of historical engraver to the queen. Foreign some years he carried on business as a print publisher in Bond Street.
Ambitious projects involved him in heavy financial losses.
He then obtained an Acting of Parliament authorising him to dispose by lottery of the collection of watercolour drawings from which his engravings were executed, together with unsold impressions of the plates, together valued at £150,000. Tomkins died at his house in Osnaburgh Street, London, on 22 April 1840.
