[7] Slevin played at second-row and scored a try in the 28-5 victory over Warrington in the 1950–51 Lancashire Cup Final during the 1950–51 season at Station Road, Swinton on Saturday 4 November 1950,[8] and played at second-row in Wigan's 10–0 victory over Barrow in the Challenge Cup Final at Wembley Stadium, London on Saturday 5 May 1951.

Slevin played at prop in the 15-10 victory over St. Helens in the 1953–54 Challenge Cup Final during the 1952–53 season at Wembley Stadium, London on Saturday 25 April 1953, in front of a crowd of 89,588,[10] and played in the 18-8 victory over Batley in the 1952–53 Yorkshire Cup Final during the 1952–53 season at Headingley, Leeds on Saturday 15 November 1952.

Slevin played at prop in the 15-8 victory over York in the 1957–58 Yorkshire Cup Final during the 1957–58 season at Headingley, Leeds on Saturday 19 October 1957,[11] played at prop in the 10–16 defeat by Wakefield Trinity in the 1960–61 Yorkshire Cup Final during the 1960–61 season at Headingley, Leeds on Saturday 29 October 1960.

Only five rugby league footballers have won "All Six Cups" during their career, they are; Aubrey Casewell (while at Salford and Leeds), Alan Edwards (while at Salford and Bradford Northern), John Etty (while at Oldham and Wakefield Trinity), Ted Slevin (while at Wigan and Huddersfield), and Derek Turner (while at Oldham and Wakefield Trinity).

[15] Along with William "Billy" Banks, Edward "Ted" Cahill, Gordon Haynes, Keith Holliday, William "Billy" Ivison, Robert "Bob" Kelly, John McKeown and George Parsons, Slevin's only Great Britain appearances came against France prior to 1957, these matches were not considered as Test matches by the Rugby Football League, and consequently caps were not awarded.