Green’s Dictionary of Slang

itching jenny n.

the vagina.

1890–1904		Farmer & Henley Sl. and Its Analogues.
1980		Maledicta IV:2 (Winter) 185: The elliptic mood is still sometimes found, however, in the advertisements of those on the game, where they delicately refer to Miss Brown, Madam Brown, Itching Jenny, Mary Lane, Madge Howlett and Miss Laycock in shop-window come-ons.