Living (or eating) high on (or off) the hog is an American expression. High has been in used in the UK with the meaning impressive; superlative; attractive since the 17th century and in the USA since the early 19th century. For example, this from Samuel Pepys Diary, or as he liked to call it Samuel Pepys' Memoirs. Comprising his diary from 1659 to 1669, and a selection from his private correspondence (from the entry for 29th July 1667):
"Where it seems people do drink high."
A US citation is George G. Foster's New York in Slices, 1848:
"I say Jim! ain't this high?"
'High on the hog' is to attributed to the American writer H. L. (Henry Louis) Mencken in the Nevada State Journal, December 1941:
"There was the customary amount of tear-shedding over business, but certain shows prospered. Among those still eating high on the hog - to filch a dandy from Mr. Mencken - are 'Sons of Fun', Let's Face It'..."
I've checked this with the Mencken Society and they can't confirm that attribution. Mencken did use the phrase in The American Language, 1919, but appears there to be referring to it only as an existing phrase:
"New verb phrases of a more elaborate sort are coming in all the time, e.g., to go Hollywood, to bottom out, to pull a fast one, to pitch woo (to make love) and to eat a little higher on the hog."