Green’s Dictionary of Slang

sleek and slum (shop) n.

[SE sleek, i.e. a well-dressed, ‘smooth’ man + slum n.2 (3), i.e. the tricks the woman might play or slum n.1 (1)]

a public house frequented by ‘single men and their wives’ (Bee), i.e. prostitutes and their male clients.

Show quotations
[UK]‘Jon Bee’ Dict. of the Turf, the Ring, the Chase, etc. 161: Sleek and slum shop a public-house or tavern where ‘single men and their wives resort’.