I heard Stan Hugill assert, at a festival, that Drunken Sailor was a "stamp and go" chantey, used on British ships with big crews. The stamp and go technique of hauling a halyard had the crew line up along the halyard, which was laid out upon the deck. They faced away from the standing portion and, picking up the line, walked away in rhythym, stamping and singing. When a sailor went as far as he could go, he dropped the line and ran back to the block, picking up the halyard again. So, with a big enough crew you'd get a sort of conveyorbelt effect. The march tempo of Drunken Sailor lends itself to this practice.

The Honorable East India Company's ships were big, with large crews, and they tended to follow naval procedure more than other merchantmen. That may explain why the chantey refers to such punishment -- I don't know that merchant captains employed a "captain's daughter". Since the Royal Navy didn't allow chanteying, but the song has a touch of the navy in it, I'm inclined to agree with Hugill that it was created (or at least popularized) by John Company men.

Jerry