In 1864 he was appointed to help William Duguid Geddes with his Greek classes, but he devoted his vacations to working on philosophy. In 1866 he was appointed professor of philosophy of mind and logic at University College, London. He remained there until he was forced by ill-health to resign a few months before his death, lecturing on logic, deductive and inductive, systematic psychology and ethics.
He left little published work. A comprehensive work on Hobbes was never completed, though part of the materials were used for an article in the Encyclopædia Britannica, and another portion was published as one of Blackwood's "Philosophical Classics." Together with Bain, he edited George Grote's Aristotle, and was the editor of Mind from its foundation in 1876 till 1891. Robertson had a keen interest in German philosophy, and took every opportunity to make German works on English writers known in the United Kingdom. In philosophy he was principally a follower of Bain and John Stuart Mill. He and his wife (a daughter of Mr Justice Crompton) were involved in many kinds of social work; he sat on the Committee of the National Society for Women's Suffrage, and was actively associated with its president, John Stuart Mill. He also supported the admission of women students to University College.