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Related to nellies: nervous Nellies

not on your nelly

An expression of one's refusal to do something. Primarily heard in UK, Australia. A: "Will you go out to the barn and clean up after the horses?" B: "Not on your nelly!"
See also: nelly, not, on

Not on your nelly!

  (British & Australian old-fashioned)
something that you say in order to tell someone that you will not do something 'Perhaps you could take Phil with you to the party.' 'Not on your nelly!'
See also: not, on