This cue is the Stevenson Champion Cue 788 Break. It has an ash shaft on an ebony butt with a mahogany frontsplice and an ivory badge.
The cue commemorates the break of 788 made by Harry Stevenson in a match against Charles Dawson at Newcastle-upon-Tyne in April 1904.
The cue was manufactured by Cox & Yeman between 1904 and 1908, when Cox & Yeman went bankrupt and ceased to trade.
I have a similar cue which commemorates a break of 802 that Stevenson made in February 1905.