Regular City keeper Willis Walker was serving with the Royal Naval Depot at the time, and though he played for City when he could get away from London, his availability was limited.

Walker played in the first game of the season, a 4-1 defeat of Notts County on 7 September, but Cook took over between the sticks the following week, in the return with County at Meadow Lane. City lost the game 5-2, though the Yorkshire Post reported, 'Although the score against him was heavy, Cook kept a fine goal for the City, some of his saves being brilliant.'

Cook retained his place for the following five games, during which he conceded seven goals. Most of them came in a single game, the 4-2 defeat at Birmingham on 28 September. The young custodian impressed local reporters with his performances; following the 1-0 defeat at Lincoln on 19 October, the Leeds Mercury noted that 'it was the consistent good play of the backs and the really brilliant goalkeeping of Cook that saved a worse situation for Leeds City', while the Post wrote of his 'fine custodianship'.

Altogether that season, Cook made eleven appearances for City, though he was only on a winning side on three occasions.

Cook continued to act as reserve to Willis Walker after the latter was demobbed, though he never appeared for City in peacetime and joined Castleford Town following Leeds' expulsion from the League in October 1919.

In 1928, Cook signed for Stockport County and he finally made his league debut in the 1928/29 season, going on to make nine appearances in total that season before drifting out of the senior game.