Green’s Dictionary of Slang

a blow (with the head, fist or foot) to the mouth or face.

1944		O. Ferguson ‘Vocabulary for Lakes, [etc.]’ AS XIX:2 106: A Liverpool kiss is a kick in the chin.
1957		G. Kersh Fowlers End (2001) 28: You know what it is, a Liverpool kiss? Make a quick grab for the lapels o’ the coat, an’ pull somebody forward. At the same time bunt ’im in the face miv the top o’ your ’ead an’ kick ’im in the stomach miv your knee. Naturally ’e falls forward. While ’e’s falling, punch ’im in the jaw miv all your might so he gradually falls dahn senseless. Then, at your leisure, kick ’im in the ’ead.
1968		‘Hy Lit’ Hy Lit’s Unbelievable Dict. of Hip Words 50: liverpool kiss – A hit on the mouth.
1971		Canberra Times 9 Aug. 14/4: Vaughan had already been given two cautions, one for a ‘Liverpool Kiss’ and the hard forward play did not meet with the referee’s approval .
1989		H. Rawson Dict. of Invective (1991) 291: Liverpool, as in Liverpool kiss, sailor-talk for a kick in the chin.