Green’s Dictionary of Slang

tollywhacker n.

[juv. tolly, a candle (the similarity in shape) + whack v.1 (1)]

a roll of paper used as a club in children’s play.

[UK]J. Franklyn Cockney 160: An instrument termed a ‘tolly-whacker.’ This is just a roll of stiff paper. It brings forth a most satisfying thwack on making contact.