Cockett was born in Broadstairs. He attended Cambridge University and won his Blues at both cricket and hockey. As a cricketer he was a middle-order batsman while his hockey was played as a half-back.[4] He made seven first-class appearances for Cambridge University in 1951 and made a century against Sussex in Worthing to help set up a 137 run win.[5][6] From 1949 to 1962, Cockett regularly played in the Minor Counties Cricket Championship for Buckinghamshire.[7] On leaving Cambridge Cockett became a master at Felsted School, where he taught mathematics and coached cricket and hockey.[8]