Born in Dublin, Ireland, Cobbe founded the Society for the Protection of Animals Liable to Vivisection (SPALV) in 1875, the world's first organization campaigning against animal experiments. In 1898, ahe founded the British Union for the Abolition of Vivisection (BUAV). Cobbe was a member of the executive council of the London National Society for Women's Suffrage and writer of editorial columns for London newspapers on suffrage, property rights for women, and opposition to vivisection. Cobbe's first work, published anonymously, was on The Intuitive Theory of Morals (1855). She travelled in the East, and published Cities of the Past (1864), Criminals, Idiots, Women and Minors (1869), Darwinism in Morals (1872), and Scientific Spirit of the Age (1888).