Cunliffe was selected to go on the 1920 Great Britain Lions tour and 1924 Great Britain Lions tour of Australia and New Zealand. He won caps for Great Britain while at Warrington in 1920 against Australia, and New Zealand (2 matches), in 1921-22 against Australia (3 matches), in 1924 against Australia (3 matches), and New Zealand, and in 1926 against New Zealand. He also won caps for England while at Warrington in 1921 against Wales, Other Nationalities, and Australia, in 1922 against Wales, in 1923 against Wales (2 matches), in 1925 against Wales (2 matches), in 1926 against Wales, and Other Nationalities.