Green’s Dictionary of Slang

1. (US) to be quiet, to stop talking.

1855		Life in Boston & N.Y. (Boston, MA) 14 Apr. n.p.: Cork up and burst, Blower.
1866		H.L. Williams N.-Y. After Dark 36: Cork up, Ginny, and wash your glasses!
1895		J.L. Williams Princeton Stories 22: Oh, cork up, you big cow!

2. to make someone be quiet.

1884		(con. c.1840) ‘Mark Twain’ Huckleberry Finn 24: Jim would [...] say, ‘Hm! What you know ’bout witches?’ and that nigger was corked up and had to take a back seat.
1938		N. Lindsay Age Of Consent 87: He shut up suddenly, corked up by a special item in his list of martydoms that squandered him to gloom.

3. (US) to have sexual intercourse (with) .

1955

B. Appel Tough Guy [ebook] ‘He don’t look like a jewboy,’ Clip announced. ‘Some mick must’ve corked up his of lady on a dark night’.

4. (UK/UK black) to fill up.

1979		(con. 1930s) J. Wolveridge He Don’t Know ‘A’ from a Bull’s Foot 9: I heard her say ‘We can’t pay the landlord today, he’ll have to cork his arsehole up’.
1999		(con. 1979–80) A. Wheatle Brixton Rock (2004) 223: Nuff people are gonna cork up the dole house.