Green’s Dictionary of Slang

wick n.²

In phrases

get on someone’s wick (v.) [rhy. sl.; Hampton Wick = prick n. (1); a link to wick n.¹ would appear coincidental]

to irritate, to annoy.

1937		J. Curtis You’re in the Racket, Too 76: There’s only one thing gets on my wick. This here yenzing party you’re staging to-night.
1945		J. Maclaren-Ross Swag, the Spy and the Soldier in Lehmann Penguin New Writing No. 26 56: Parades and bullshit got on his wick.
1959		A. Sinclair My Friend Judas (1963) 105: This place has got on my wick. I want to get out.
1966		P. Willmott Adolescent Boys of East London (1969) 88: Some of the teachers got on my wick.
1979		D. Maitland Breaking Out 49: Maybe it’s ‘Danny Boy’ that gets on your wick.
1984		‘Derek Raymond’ He Died with His Eyes Open 63: I hate that kind of thing [...] especially when I’ve got a lot on my mind. It gets right on my wick.
1993		I. Welsh Trainspotting 273: She’s bad-mouthing Mark, which is fair enough, but it’s starting tae get oan ma wick.
1996		P. Howard The Joy (2015) [ebook] He’s getting on my wick so much.
2003		N. Griffiths Stump 178: The same line over and over. It’s getting on Alistair’s wick.