Green’s Dictionary of Slang

a very hard blow (to the face or head).

1821		‘An Amateur’ Real Life in London I 616: Randall got a konker, which tapped the claret.
1822		Caledonian Mercury 31 Oct. 4/1: Abbott appeared pefectly stupid from the repeated conkers he received.
1831		Australian (Sydney) 7 Jan. 3/5: Chalker [...] got a ‘konker’.
1832		Egan Bk of Sports 200: Sam planted cleverly a conker.
1870		Bell’s Life in Sydney 21 May 2/5: Abe received a ‘conker’ [...] which made him kiss mother earth.