Green’s Dictionary of Slang

1. a drink; thus damp bazaar, a bar.

1836–7		Dickens Pickwick Papers (1999) 356: ‘So we’ll just give ourselves a damp, Sammy.’ Saying this, Mr. Weller mixed two glasses of spirits and water.
1899–1900		C.L. Cullen Tales of the Ex-Tanks 108: As for the damps, I’ve got kags of it.
1902		C.L. Cullen More Ex-Tank Tales 13: We [went] across the street from the station to a damp bazaar.

2. the vagina, one of a number of terms that equate the organ with wetness, whether that of urine, vaginal secretions or the use of the synon. fish n.¹ (1a); thus slice of damp.

1958		Southern & Hoffenberg Candy (1970) 112: Somehow, from the gamut of emotions which crossed your face, I had the idea the stool had slipped up into your damp.
1977		Butler & Shryack Gauntlet 99: Nothin’ like a slice of damp. is there? [HDAS].