Green’s Dictionary of Slang

1. drunk.

1896		W.C. Gore Student Sl. in Cohen (1997) 13: corked a. Drunk.
1905		Sun. Times (Perth) 29 Oct. 1/3: The fizz flowed [and] more than one lucky candidate got corked to the kiss-curl.
1912		R.W. Brown ‘Word-List From Western Indiana’ in DN III:viii 573: corked, adj. Drunk.
1927		W.R. Morse ‘Stanford Expressions’ in AS II:6 276: corked — intoxicated.
1933		‘William Juniper’ True Drunkard’s Delight 231: Sufficient to encourage him as a jolly dog; that is, happy [...] corked or corky.
1960, 1975		(ref. to 1920s) Wentworth & Flexner DAS.
1970		in DARE.

2. constipated.

1996

Allsopp Dict. Carib. Eng. Usage.

3. exhausted.

1955

(con. 1939–45) J. Klaas Maybe I’m Dead 180: I’m plenty corked.

4. (UK black, also cork) absolutely full.

1999		(con. 1979–80) A. Wheatle Brixton Rock (2004) 150: Me and Floyd went to Brixton Town Hall, the place was cork.
2016		A. Wheatle Crongton Knights 233: We managed to make it out of the front room but the hallway was still corked.