Green’s Dictionary of Slang

cant v.²

to drink, to swallow.

1762		Smollett Sir Launcelot Greaves II 89: He ordered the waiter [...] to bear a hand, ship his oars, mind his helm, and bring alongside a short allowance of brandy or grog, that he might cant a slug into his bread-room.
1788, 1796		Grose Classical Dict. of the Vulgar Tongue (2nd, 3rd edn) n.p.: Cant [...] drink a dram.
1811		Lex. Balatronicum.
1823		Egan Grose’s Classical Dict. of the Vulgar Tongue.

In phrases

cant a slug into your bread-room

to drink a glassful of spirits.

c.1786

Grose Classical Dict. of the Vulgar Tongue ms. additions n.p.: Cant a slug into your bread-Room. Drink a Dram. Sea term.