He was articled to the engraver Joseph Collyer the younger, an exacting master who required steady application from his pupil - as a result, Heath acquired a great mechanical skill in his art.

He made many engravings after artists such as Stothard, Smirke, and others, and these were to be found in publications such as: Sharpe's British Classics, the Lady's Poetical Magazine,[2] Forster's Arabian Nights, Glover's Leonidas, and many similar editions of popular works.

He engraved some large plates, notably "The Dead Soldier" (after Joseph Wright of Derby), "The Death of Nelson" (after Benjamin West), "The Riots in Broad Street.

He re-engraved the existing set of Hogarth's plates, and completed the engravings of Stothard's "Canterbury Pilgrims", left unfinished by Schiavonetti at his death.

His portraits were painted by Joshua Reynolds, James Lonsdale (1777–1839), William Behnes, L. F. Abbott, and Thomas George (fl.