Graham Eccles played in Leeds' 12-24 defeat by St Helens in the Championship Final during the 1969–70 season at Odsal Stadium, Bradford on Saturday 16 May 1970, and in the 9-5 victory over St. Helens in the Championship Final during the 1971–72 season at Station Road, Swinton on Saturday 20 May 1972.
Graham Eccles played left-second-row in Leeds' 16-7 victory over Widnes in the 1976–77 Challenge Cup Final during the 1976–77 season at Wembley Stadium, London on Saturday 7 May 1977, in front of a crowd of 80,871, and played left-second-row in the 14-12 victory over St. Helens in the 1977–78 Challenge Cup Final during the 1977–78 season at Wembley Stadium, London on Saturday 13 May 1978, in front of a crowd of 96,000.
Graham Eccles played right-second-row and scored a try in Leeds' 36-9 victory over Dewsbury in the 1972–73 Yorkshire Cup Final during the 1972–73 season at Odsal Stadium, Bradford on Saturday 7 October 1972, played left-second-row in the 7-2 victory over Wakefield Trinity in the 1973–74 Yorkshire Cup Final during the 1973–74 season at Headingley, Leeds on Saturday 20 October 1973, played left-second-row in the 15-11 victory over Hull Kingston Rovers in the 1975–76 Yorkshire Cup Final during the 1975–76 season at Headingley, Leeds on Saturday 15 November 1975, played left-second-row, and scored a try in the 16-12 victory over Featherstone Rovers in the 1976–77 Yorkshire Cup Final during the 1976–77 season at Headingley, Leeds on Saturday 16 October 1976, played left-second-row in the 15-6 victory over Halifax in the 1979–80 Yorkshire Cup Final during the 1979–80 season at Headingley, Leeds on Saturday 27 October 1979, and played left-second-row in the 8-7 victory over Hull Kingston Rovers in the 1980–81 Yorkshire Cup Final during the 1980–81 season at Fartown Ground, Huddersfield on Saturday 8 November 1980.
Graham Eccles played loose forward in Leeds' 12-7 victory over Salford in the 1972–73 Player's No.6 Trophy Final during the 1972–73 season at Fartown Ground, Huddersfield on Saturday 24 March 1973.
[citation needed] Graham Eccles scored a try on his début for Leeds', as did fellow débutante Phil Cookson, against Bradford Northern on Saturday 19 April 1969.