Heath was the son of James Heath (1757 - 1834), an Associate of the Royal Academy, who taught him how to etch as a child.
As an adult Charles engraved plates for bank notes and stamps as well as producing fine art prints. He was the first engraver to use steel rather than copper for his plates. Steel plates were more resistant than copper. This meant more prints could be produced from them before they were worn out.
Heath worked closely with JMW Turner (1775 - 1851) on several publications. He engraved and published 'Turner’s Annual Tour: Wanderings by the Loire' on 1 June 1833. He also oversaw the engraving of many of Turner's watercolours by other engravers. He also promoted the print series 'Picturesque Views in England and Wales', which Turner had worked on.