Green’s Dictionary of Slang

to beat, to ruin, to dispose of, to ‘put paid’ to.

1876		J. Greenwood Low-Life Deeps 213: It’s summat in the mortar that works its way into your cistern, and that’s what’ll bunnick up old Cooper.
1885		‘’Arry on the Elections’ in Punch 12 Dec. 277/2: And I think I’ve give Gladstone his gruel, and bunnicked up Brummagem Joe.
1892		‘’Arry in Venice’ in Punch 27 May 88/1: Hinfluenzas, Helections, and cetrer, has bloomin’ nigh bunnicked up Trade.