Utter Barrister, Lincoln's Inn, London, 1955.
He was Chief Justice of the Eastern Caribbean Supreme Court from 1984 until his retirement in 1991. In 1955, he was called to bar of England and Wales at the Lincoln’s Inn. He returned to Jamaica and worked as a Crown lawyers from 1955 to 1962.
He became a magistrate in the Jamaican courts in 1962, and was promoted to the position of High Court Judge 1964.
In 1979, Robotham left Jamaica after being appointed to be a High Court Judge of the Eastern Caribbean Supreme Court by the Judicial and Legal Services Commission of the Caribbean Community. His first assignment was to reside in and hear cases from Antigua and Barbuda.
He became a Justice of Appeal of the Court in 1982, and in 1984 he became the Chief Justice. As Chief Justice, Robotham was the supreme judicial officer of the courts of Anguilla, Antigua and Barbuda, the British Virgin Islands, Dominica, Grenada, Montserrat, Saint Kitts and Nevis, Saint Lucia, and Saint Vincent and the Grenadines.
Robotham was knighted by Queen Elizabeth II in 1987.
He retired in 1991, and was succeeded as Chief Justice by Vincent Floissac. After his retirement from the Caribbean court, he was appointed to be a judge on the Court of Appeal of Belize.
In 1976, he became a member of the Jamaican Court of Appeal.
Married Gloria Angella Stiebel, June 11, 1949. Children: Gordon Michael, Rosemarie Angella.