The Half Moon was a small Wilson's pub at the top end of Holland Street, also shown here at the archives in 1963. This street still runs through Miles Platting from Butler Street to Varley Street (and has the still-surviving Navigation pub), but in the past it continued on to meet up with Hulme Hall Lane (Alan Turing Way). The Half Moon was at the Hulme Hall Lane end near Royle's Bridge over the canal, and was described as having the smallest bar room in the area - if there were half a dozen drinkers in the bar it was overcrowded [1].
1. Just Henry - Memories of Bradford and Moston Collieries Manchester, Henry Bairsto (1991).