dukey, n.¹ — Green’s Dictionary of Slang

dukey n.¹

[a particular theatre whose Jewish proprietor had a large nose, i.e. a dook n.¹ (1)]

a cheap theatre or music-hall.

1857		Paul Pry (London) 15 Aug. 3: Mr Hall [...] an ingenious ventriloquist, is too well known at every gaff and ‘dukey’ throughout the metropolis [...] to need any comment from us.
1873		Sl. Dict.
1909		(ref. to 1840s) J. Ware Passing Eng. of the Victorian Era 120/1: Dukey (Street, Boys’). A penny gaff. The four-farthing theatre obtained this title from a Jewish proprietor of one of these temples of art. His nose was very prominent.