Green’s Dictionary of Slang

a Wills Woodbine cigarette.

1948		J. O’Connor Come Day – Go Day (1984) 79: Some of them may be a wee bit damp. [...] He opened the Woodbine boxes. ‘The ould Woods were lucky, eh? Not a drop.’.
1950		C. Harris Three-Ha’Pence to the Angel 160: A world pungent with the smoke of Woods.
1956		S. Selvon Lonely Londoners 43: Cap only smoking Benson and Hedges — if you offer him a Woods he would scorn you.
1957		S. Selvon Ways of Sunlight 133: The Englishman lean back in his chair, smoking a Lighthouse, which is the Barbadian equivalent to a Woods.
1965		S. Selvon Housing Lark 54: I change my brand. I only carry Woods now – and filter tip.