Green’s Dictionary of Slang

a form of illicit street-selling by which the buyer purchases a straw, usu. for one penny, and is given, as a ‘free gift’, a pamphlet (either pornographic or political) or a ‘gold’ ring, neither of which items, the seller claims, are they allowed to sell; thus strawer n., the seller.

1859		Hotten Dict. of Modern Sl. etc. 103: strawing selling straws in the streets (generally for a penny), and giving the purchaser a paper (indecent or political) or a gold (!) ring, ? neither of which, the patterer states, he is allowed to sell.
1861		(con. 1840s–50s) H. Mayhew London Labour and London Poor I 215/1: Akin to this ‘board work’ is the practice of what is called ‘strawing,’ or selling straws in the street. [Ibid.] 239: The strawer offers to sell any passer by in the streets a straw and to give the purchaser a paper which he dares not sell [...] he intimates that the paper is political, libellous, irreligious, or indecent.
1870		Hotten Sl. Dict.