I'd doubt if the sailors on ships from British ports would have given a toss about the rights and wrongs of the past wars with America, especially since they'd have come from all sorts of places. But I imagine they might have like taking the piss out of any Yankee sailormen (and they'd have been Yankees wherever they came from in the States), and backing Santy Anna in the song might have been a way of doing that.

And anyway Santy Anna is a much more splendid sort of a name than Zachary Taylor. And the underdog winning is always a better story, even if it doesn't happen that often in real life.