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
See:
http://www.english-for-students.com/Cockney-Rhyming-Slang-N.html
Steve
by SteveB47 March 25, 2009