Green’s Dictionary of Slang

duke n.²

gin.

1853		Dickens ‘Slang’ in Household Words 24 Sept. 75/2: For one article of drink, gin, we have [...] duke, jackey, tape, blue-ruin, cream of the valley, white satin, old Tom.
1864, 1867, 1870		Hotten Sl. Dict.

SE in slang uses

In phrases

touch of the duke (n.) [i.e. the stiff-backed erect posture of the aristocracy]

an erection.

1971

(con. WWII) B. Aldiss Soldier Erect 167: I’m just wanking myself silly. I’ve only got to move and I get a touch of the duke.