Cooke was born in Melbourne, Australia, but educated at Tonbridge School in Kent, England.
[1] A slow left-arm spinner who usually opened the bowling, Cooke began playing for Otago soon after he arrived in Dunedin, appearing in the annual match against Canterbury in January 1880 at the age of 17.
[4] In his three first-class matches in 1883–84, two against the touring Tasmanian team and one against Canterbury, he took 29 wickets at an average of 9.41.
[7] In Nelson's next match, in 1886–87, he took 5 for 27 and 4 for 50 and made his highest first-class score of 34, but this time Wellington won.
[2] He was one of the group that acquired the land and developed Palmerston North's major cricket ground, now known as Fitzherbert Park.