Your first clue was this player’s surname, “cock”, which is one of the names for a shuttlecock, that curious mix of ball, feathers and cage that lofts back and forth across the net to score the points. Other names for it are a bird, or a birdie (referring to the feathers, which, I am very glad to say, are now more often synthetic or plastic) - or a shuttle (referring to its cage-like construction, and also, more recently, to the way it is shuttled back and forth across the net like the shuttle did in weaving cloth).
You may be amused to learn that at one time the "u" was an "i" but, for whatever reason, this version is no longer used.
Curious it may look, but the shape is very aerodynamic, and however it sets off on its flight towards its target it will almost immediately turn, by magic, and fly with the cork part, the rounded end, leading, and the feathers propelling it along from behind.
Bit of a hunt for this set but it is catalogued, at the back of the book, in our original British Trade Index part I as :
FOOTBALLERS (A). Sm. 80 x 38. Hand-coloured glossy photos. Back illustrated at Fig. ZA10-3. Unnd. (18). Issued with “Adventure”.
There then follows this list :
In our updated British Trade Index it has been restored amongst its Thompson stable-mates, and is catalogued as :
FOOTBALLERS (A). (AD). 1922. 80 x 38. Hand-coloured glossy photos. Unnd. (18). See HT-36. Back headed “With the Editor`s Compliments”. Anonymous.