Steele-Bodger played for Cambridge in the Varsity Match in 1945 and 1946. He then represented the Edinburgh University rugby club for two full seasons. His brother Alasdair also played for Edinburgh University.
He gained 9 caps for England, playing in all 4 matches in the 1946-47 season and all 5 matches in the 1947-48 season. In his final international, against France in March 1948, Steele-Bodger had to move to scrum-half when Richard Madge left the field, despite suffering from concussion himself.[3] An anterior cruciate ligament injury ended his playing career in 1949. Subsequently, he was a selector for England and The Lions, President of the Rugby Football Union in 1973-74, and Chairman of the International Rugby Board.
In 1948, he inaugurated the annual tradition of bringing a guest Steele-Bodger XV to play Cambridge University as a warm-up to the Varsity Match.
He was an active member of the Round Table being one of the founding members of his local Tamworth Round Table in 1952.