Dickenson obtained her B.A. in political science from Wellesley College, Boston, and an M.Sc. in international relations from the London School of Economics. She returned to the U.S. to work as a research assistant at Yale University, and spent a year working for the Vera Institute of Justice in New York City. In or around 1975, she took up a post at the Open University in the UK, and obtained her doctorate in philosophy with a study on moral luck in ethics and politics. She worked as a lecturer at the Open University for 22 years.

In 1997, she moved to Imperial College, London as Leverhulme Reader in Medical Ethics and Law, and in 2001 to the University of Birmingham as John Ferguson Professor of Global Ethics. In 2005, she became Professor of Medical Ethics and Humanities at Birkbeck College, London, where she directed the Birkbeck Institute for the Humanities. She also directed four international research projects for the European Commission, including the Network for European Women's Rights.

In 2006, she became the first woman to receive the International Spinoza Lens prize, a bi-annual prize in ethics awarded in the Netherlands.