Cove-Smith was a talented schoolboy player at Merchant Taylors School, and carried that talent through to university, playing in three Varsity Matches for Cambridge University from 1919 to 1921, winning his sporting 'Blue'. He led the 1924 British Lions tour to South Africa, losing three of the four tests and drawing one. As captain, he led England to the 1928 Grand Slam and he was inducted onto the World Rugby Museum Wall of Fame in 2001.