a shortened version of "Nelly Duff". Nelly Duff = puff (breath) in Cockney rhyming slang. 'Not on your Nelly' is used to mean 'Not on your life'. "Breath" is synecdochical for "life"

See:
http://www.english-for-students.com/Cockney-Rhyming-Slang-N.html

Steve
There is no way you are going to get money out of me. Not on your nellie.
by SteveB47 March 25, 2009
a yorkshire expression, meaning, you will not go. basically 'i will not'
babs: jean, do you want to go shopping?
jean: not on your nellie love!
by alex-girl January 03, 2009

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