Green’s Dictionary of Slang

1. a prostitute (in UK those who specialized in army camps).

1842		Nichols Wkly Arena (NY) 4 June) n.p.: The two following [songs] struck us as being particularly rich, rare, and racy: — the ‘Lovesick Tommy’ and the ‘Benighted Wren’.
1869		J. Greenwood Seven Curses of London 292: The colony of women who ‘squatted’ amongst the furze of Curragh Common, and subsisted on such miserable wage as the soldiers there quartered could afford to pay them. These creatures are known in and about the great military camp and its neighbourhood as ‘wrens.’.

2. (US) an attractive woman.

1911		T.A. Dorgan in Zwilling TAD Lex. (1993) 89: Hey judge, there’s a swell wren down in the water named Edith — go down and make her.
1920		S. Lewis Main Street (1921) 312: Me and Harry Haydock are going to take her and that fat wren that works in the Bon Ton.
1930		E. Glyn Flirt and Flapper 72: Flapper: He’s gone plumb nuts about this little wren.
1936		R. Chandler ‘Goldfish’ in Red Wind (1946) 159: ‘Who was the wren?’ I asked.
1945		R.L. Bellem ‘Coffin for a Coward’ in Hollywood Detective Dec. 🌐 I recognized the wren. She was Janet Moore, the Bonham kid’s co-star.
1962		Ragen & Finston World’s Toughest Prison 823: wren – A young woman or girl.