This is a William Cook's Model Cue. It has a mahogany butt hand-spliced onto an ash shaft.
The cue refers to William Cook Senior, who defeated John Roberts Senior on 11 February 1870 to become Professional Champion at the age of nineteen.
This type of cue was made by Thurston & Co, from the 1870s onwards. The example shown in the photograph probably dates from the late 1890s or early 1900s.