Green’s Dictionary of Slang

oily (rag) n.

a cigarette.

1932		‘P.P.’ Rhy. Sl.
1958		Galton & Simpson ‘Hancock’s War’ in Hancock’s Half-Hour May [radio script] Do you want an oily rag...er...a fag?
1961		Galton & Simpson ‘The Train Journey’ Hancock’s Half-Hour [TV script] sid: Do you fancy stretching your legs [...] just down the corridor for a cough and a draw? lady: A what? sid: An oily rag . . . a snout . . . fag.
1971		Daily Tel. 17 Sept. n.p.: oily rag = ‘fag’.
1981		P. Wright Cockney Dialect and Sl. 103: oily rag ‘fag’.
2005		P. Howard Curious Incident of the Dog in the Nightdress 161: All the [...] fit-looking birds are all to be found outside the front door [...] sucking on the old oily rags.