Mudge was coached by former Great Britain rugby league test captain, Gus Risman. A back-rower, or prop, Rupert Mudge played left-second-row, i.e. number 11, and scored a tryin Workington Town's 18-10 victory over Featherstone Rovers in the 1952 Challenge Cup Final during the 1951–52 season at Wembley Stadium, London on Saturday 19 April 1952, in front of a crowd of 72,093.
Three Australian footballers were in the Workington Town side, including Rupert, Tony Paskins, and Bevan Wilson. They played the match in front of Anthony Eden, who was Foreign Minister in the Government and Rupert John Mudge scored the longest ever running try at Wembley, which was the turning point in the match. It was then added to when Aussie team mate Tony Paskins, and George Wilson together scored another try in the final minutes of the game and Workington Town team beat Featherstone and won.
Rupert Mudge played left-second-row, i.e. number 11, in Workington Town's 12-21 defeat by Barrow in the 1955 Challenge Cup Final during the 1954-55 season at Wembley Stadium, London on Saturday 30 April 1955, in front of a crowd of 66,513.
In 1955 both Mudge and Paskins returned to Australia where they joined the Eastern Suburbs rugby league team, Paskins was appointed captain. Mudge who played 45 matches for the Eastern Suburbs club in the years (1955–58) is recognised as that clubs 448th player.
After his retirement from football Rupert spent some years as a panelist on the Channel Seven Rugby League panel discussion program "Controversy Corner" hosted by Rex (the Moose) Mossop.
In his professional life in Australia, besides football, he worked for P.Rowe Pty. Ltd.
He married his Australian sweetheart, Yvonne Rita Trenerry, who had followed him to England in Workington Town where they lived until 1955 when they returned to Australia to live at Coogee Beach. They had two children, Barbara and John.