Green’s Dictionary of Slang

broomstick n.

[supposed resemblance]

1. the penis.

[UK]Partridge DSUE (1984) 139/1: C.19–20.

2. a gun or rifle [it also ‘cleans up’].

[UK]J. Ware Passing Eng. of the Victorian Era 50/1: Broomstick (Canadian). A gun or rifle. No word could more perfectly outline the peaceful character of the Canadian as distinct from his American brother, when it is borne in mind that the latter calls his gun, shooting iron.
http://taskandpurpose.com (US) 12 Oct. 🌐 Most people would be content with calling a firearm by what it is: rifle, shotgun, machine gun, or pistol. But no, in the Army, we have to give special names that sound like they come from a 4-year-old. Ergo, the boomstick, most usually a name for a rifle or shotgun.
410 ‘Civilians’ 🎵 Had a young boy with a broomstick / In the room with a pump.
[UK]Digga D. ‘G Lock’ 🎵 I cross the Blue bridge, clart off two quick (Bap) / Then park the broomstick [...] (Bap, bap, boom).