A pot of jam

Henry Farrell writes, apropos of an article in the Guardian:

There's a bit of language play there that may escape non-UK/Irish readers. "Jammy" in "jammy first-timers" means 'possessed of undeserved luck.' It's almost never used afaik except as part of the phrase "jammy bastard."

I was just thinking the other day of this lyric from the musical "Sweet Charity":

All I can say is "Wow-ee!"
Look-a where I am.
Tonight I landed, pow!
Right in a pot of jam.
What a set up! Holy cow!
They'd never believe it,
If my friends could see me now!

In particular, I was thinking that I had never heard the expression "land in a pot of jam" to mean lucky in any other context. (The lyricist, Dorothy Fields, was an American, not a Brit.) Perhaps there's some connection.