This is a William Cook Facsimile Cue. It has an ash shaft with a massive hand-spliced ebony butt. The butt has a circumference of 5 inches.
The badge appears to have been made of whalebone or something similar. It states that the cue is a facsimile of the cue used by William Cook (Senior).
The cue was made by J Ashcroft & Co of Liverpool, at some time in the period from 1884 to the late 1890s.
Interestingly, Ashcroft & Co employed William Cook's son, William Cook Junior, as a billiards tutor at the start of his professional career in the 1890s.