Born at St Pancras, Middlesex, Cox was the fourth son of Thomas Henry Whitmore Cox, an art printer, and his first job after leaving school was as a clerk to a silk merchant in the City of London.
At the St Pancras Industrial Exhibition of 1880, he entered a crayon drawing and won a silver medal.
In 1882, Ballin moved to Copenhagen, to take up appointment as Engraver-Royal to the King of Denmark, and Cox began to earn his living as an etcher working on his own.
In the 1890s, he attended photogravure classes at the Regent Street Polytechnic and got a job with Graves and Fores.
[1][2] Cox gained skill as an engraver, specializing in colour mezzotints, reproducing works by contemporaries and old masters.