Dixon was educated at Eton and Grenoble in France. After university, he served with the Grenadier Guards from 1954 to 1966 including service in the Cyprus Emergency
In 1964 Dixon was granted leave from the army to participate in the 1964 Winter Olympics at Innsbruck and it was here that he won the gold medal in the Two-man Bobsleigh as brakeman to Tony Nash and was awarded a MBE a year later. Nash and Dixon also won three medals in the two-man event at the FIBT World Championships with one gold (1965) and two bronzes (1963, 1966).
Dixon retained his sporting links throughout his life: he was President of the Jury at the 1976 Winter Olympics, set up the Ulster Games Foundation in 1983, and was appointed Chairman of the Northern Ireland Tall Ships Council in 1987. He has been President of the British Bobsleigh Association since 1987.
Dixon retired from the army in 1966 with the rank of Major and went on to work for Kodak in their public relations department and in 1971 joined the Northern Irish business, Redland Tile and Brick Ltd, which he built up into a multimillion-pound subsidiary of Redland plc and became Managing Director. In 1983, he was appointed High Sheriff of Antrim.
Upon the death of his father, the 2nd Baron Glentoran, Dixon inherited his title and retired from business in 1998.
Dixon was Chairman of Positively Belfast from 1992 to 1996, Chairman of the "Growing a Green Economy" Committee from 1993 to 1995 and has been Shadow Minister for Northern Ireland, Shadow Minister for Sport and Shadow Minister for Environment, Food and Rural Affairs. He is also a member of the British-Irish Parliamentary Body.
Lord Glentoran is a representative peer, one of 92 hereditary peers that remain in the House of Lords after the passing of the House of Lords Act 1999, and sits on the Conservative benches.
Lord Glentoran has three sons from his first wife, Rona (divorced in 1975), and lives with his third wife, Margaret, in their family home, Drumadarragh House, near Ballyclare. His eldest son, Daniel, has two sons; his second, Andrew, a son and a daughter, and his youngest, Patrick, has one daughter. Shops at Local store Spar parkgate, particularly like the village butchers in store.
Dixon and his driver, Tony Nash, were inducted into the British Bobsleigh Hall of Fame as a result of their success. A curve at the St. Moritz-Celerina Olympic Bobrun is named for both Nash and Dixon. He was appointed a CBE in 1993 for services to Northern Ireland and Industry.