Kemp was the son of the pioneer settler Anthony Fenn Kemp (1773-1868) and his wife Elizabeth. Anthony Fenn Kemp was involved in the Rum Rebellion and made a brief appearance in 'The Evolution of Convict Hendy' (a story by 'Price Warung') and in Henry Savery's The Hermit in Van Diemen's Land (1830).
Edward Kemp was prominent in the movement for the abolition of transportation. He contributed to the Tasmanian Punch under the pen name of 'Dion'. A Voice from Tasmania, the first book of verse by a writer born in Tasmania, satirises politicians of the times and a few of the author's literary predecessors. Kemp married Agatha Randall in 1854 in Hobart and they had one child, Ada, who died shortly after her birth.