Green’s Dictionary of Slang

madge n.

1. a woman.

[UK]Appius and Virginia in Farmer (1908) 12: And all for Maud Mumble-turd, that mange-pudding Madge.
[Ire]Stanyhurst Of Virgil his Æneis VI: What shall I doo therefore? Shall I now, lyk a castaway milkmadge, On mye wooers formoure bee fawning?
[UK]G. Peele Sir Clyomon and Sir Clamydes in Dyce (1861) 516: Thous go to church in this coat bevore Madge a Sunday in her grey gown.

2. (also madgery) the female genitals.

[UK]Grose Classical Dict. of the Vulgar Tongue.
[UK]‘Ladies’ Wigs’ in Hilaria 82: Pray, ma’am, does the colour of your scratch / WEith the hair of your madgery match?
[UK]late 17C ballad q. in Sporting World 19 Apr. 49/2: Her ruffledum, puffledum, frizzledum madge.
[UK]Tilly Touchitt 32: He proceeded [...] to gratify his sight and touch, with every particularity poor Madge could discover to him.

3. (UK Und.) a homosexual man.

[UK]H.T. Potter New Dict. Cant (1795) n.p.: madge a sodomite.

4. see Madge Howlet n. (1)

In compounds

madge-cull (n.) [cull n.1 (4)]

(UK Und.) a homosexual man.

[UK]G. Parker View of Society II 85: Madge Culls. This is one of the most abandoned and infamous characters that disgrace Society [...] The name of the vice which is here intended is better omitted than experienced.
[UK]H.T. Potter New Dict. Cant (1795) n.p.: madge cull a buggerer.
[UK]Lex. Balatronicum.
[Aus]G. Seal Lingo 115: There seems to have been no shortage of terms used either by homosexuals themselves and/or by non-homosexuals, such as [...] margery, mary-ann, madge-cull and, what was once the great Australian insult, poofter.
madge-ken (n.) [ken n.1 (1), lit. ‘woman-place’]

the vagina.