Very intoxicated indeed; a drunken man “sobered” by drinking more. The feast of St. Martin (November 11) used to be held as a day of great debauch. Hence Baxter uses the word Martin as a synonym of a drunkard:
“The language of Martin is there [in heaven] a stranger” —Saint's Rest.
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894