Green’s Dictionary of Slang

snack v.2

[snack n.1 (3)]

to nag, to criticize.

[UK]Sl. Dict. 298: Snack to quiz or chaff with regard to a particular weakness or recent transaction.
[UK]Daily Tel. 6 Oct. 2: Now, I’ve got to come home boozed, don’t you know, and you are sitting up for me, and you begin to snack me about it, and then there’s a jolly row.