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1.
cockney rhyming slang for not on your life. nelly rhymes with smelly, which leads to smelly breath, breath leads to breathing to keep alive, leading to not on your life.
Martin: 'will you stroke my furry badger?'

Jon: 'Not on your nelly!'
by MsMatronic July 17, 2005
 
2.
A term (predominately Scottish) meaning "not likely" or "Fuck off home, you hairy gay"
Oli: Heard i get to jump in your eye today...
Scott: Not on your nelly!
by LordBlunkey June 16, 2004