In 1891, he became the secretary and librarian to the Institute of Jamaica in Kingston, writing extensively on the history of the island.

[2][3] After attending private schools, he gained admission to King's College London, leaving in 1875.

His son was Joseph Leslie Cundall, who became the Attorney General of Jamaica, and his daughter Frances married Guy Weihen of Munro College, Saint Elizabeth Parish.

[1] From 1876 to 1882, Cundall was the assistant editor for the revised edition of Bryan's Dictionary of Painters and Engravers (London, George Bell).

[3] In 1886, he was the editor with Sir Philip Cunliffe-Owen of the report of the Royal Commission of the Colonial and Indian Exhibition.