Cobbe was born in Dublin, Ireland, and educated at home, at Newbridge House, county Dublin, except for two years at a school in Brighton: she hated the school. After she left, she kept house for her mother and father, and after her mother's death for her father alone, for nineteen years, while she energetically educated herself. Cobbe wrote that she inherited from her parents a physical frame which, 'however defective ...from the aesthetic point of view', had been, as regards health and energy, 'a source of endless enjoyment'. Darwin's friend Joseph Dalton Hooker referred to her in a letter to Darwin as a 'disenchanting mountain of flesh'. Cobbe, however, was opposed to corsets, and to the female invalidism she believed they caused. When Cobbe's father died she inherited a very small annuity (a brother inherited the house).
She spent some time travelling, then returned to England and became involved in a couple of charitable ventures, before setting up house in London with a Welsh woman, Mary Lloyd, whom she had first met in Italy. Cobbe worked as a journalist and became involved with the women's suffrage and anti-vivisection causes. She founded the British Union Against Vivisection.