Born in Dublin, Cobbe's mother died when she was very young, and she lived with her father, a landowner and magistrate, until he died in 1857. She was tutored privately and then sent to a boarding school in Brighton.

After his death, she moved to Brighton, England, where she had previously been a student at a boarding school. She also traveled some, to places such as Italy and Egypt, and from her travels wrote several works such as Cities from the Past and Italics. Back from her travels, she moved to Bristol and began to teach in Mary Carpenter's school, working with girls released from prison, inmates of work houses, prostitutes, and other unfortunates.

From the 1860s she was a committed feminist, writing on such areas as wife-battering and the exclusion of women from the vote. Cobbe did argue fervently for women's liberation, in society as well as in the home. Many of her writings, including The Final Cause of Women, published in 1869, present bold and modern ideas about women's individualism and autonomy.

Cobbe wrote other works including The Duties of Women, and Criminals, Idiots, Women and Minors. Is the Classification Sound? A Discussion on the Laws Concerning the Property of Married Women in which she speaks out against wife-abuse and neglect.

From the 1870s Cobbe was a devoted anti-vivisectionist, campaigning energetically against the use of live animals in scientific research. She was the founder of the Victorian Street Society for the Protection of Animals from Vivisection and the president of the British Union for the Abolition of Vivisection, showing her aversion to animal experimentation.

Never married, Cobbe lived with Mary Lloyd in Bristol for 34 years, until Lloyd's death in 1896. She wrote the following passionate and (for the time) remarkably explicit Valentine poem to Lloyd in 1873:

Hereafter, when slow ebbs the tide
And age drains out my strength and pride
And dim-grown eyes and trembling hand
       I'll want you, Mary.

In joy and grief, in good and ill,
Friend of my heart! I need you still,
My PLaymate, Friend, Companion, Love,
To dwell with here, to clasp above
       I'll want you, Mary.

Quote source: Collis, R.., Lesbian Portraits. MQ Publications, 1997