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1.
Cockney Rhyming slang for saying that you are on your own.
"Who are you with?"

"I'm on my Jack Jones man - nuttin' going on."
by alarm clock May 28, 2004
 
2.
All alone
I was sat there on my Jack Jones, like a right billy no mates
by pony June 16, 2003
 
3.
See also
on my tod
I was sitting there on my tod
by Debs August 08, 2003