Green’s Dictionary of Slang

1. any cheap cigarette, irrespective of brand.

1910		‘Doss Chiderdoss’ ‘Larcenous Laura’ Sporting Times 12 Nov. 1/3: He recked not of the ‘Woodbines’ in her left-hand ‘daisy root,’ / Nor the wad of postal orders in her right!
1915		Mercury (Hobart, Tas.) 2 Nov. 3/7: You should hear the major shout / Put those — woodbines out.
1920		Register (Adelaide) 6 Apr. 4/7: In front of me was a British soldier [...] He took a ‘woodbine’ out of his pocket and put it in his mouth.
1930		(con. 1916) Sun. Times (Perth) 21 Dec. 20/7: Men huddled together in their trench [...] ‘Chuck us a woodbine, Mac!’ said the youngster.

2. (Aus.) an Englishman, esp. a soldier.

1919		W.H. Downing Digger Dialects 54: woodbine (n.) — An English soldier, so called from the name of a cheap brand of cigarettes favored by Englishmen.
1921		Sun. Times (Perth) 10 July 4/7: First Woodbine last Wednesday: ‘Who won the Test match?’ Second Woodbine: ‘The —s that won the War’.
1924		(con. WWI) A.G. Pretty Gloss. Sl. [...] in the A.I.F. 1921–1924 (rev. t/s) n.p.: woodbine. A cheap brand of cigarettes so popular amongst English troops that the name became a commonly used nickname for English troops.
1933		A.E. Strong in Partridge Sl. Today and Yesterday 288: I think he is a Woodbine, but he will do me for a tin plate.
1938		Queenslander (Brisbane) 11 May 14/3: ‘I’ve got a Blighty pass [...] but it isn’t any good to me,’ said our ‘Woodbine’ friend. ‘I’ve got no money’.
1941		Baker Popular Dict. Aus. Sl.
1988		(ref. to WWI) McGill Dict. of Kiwi Sl. 124/2: Woodbines Anzacs’ name for British troops WWI, because they smoked the cheap Wills Woodbine cigarettes; later applied to any Englishman.
2003		McGill Reed Dict. of N.Z. Sl. [as cit. 1988].