There has been one instance on WW, as far as I can see, of this colourful phrase being used (by Bob). I suddenly realised that I didn't know its derivation.
As one might guess from the fact that it sounds so daft and incongruous, it's from rhyming slang:
not on your nelly:
(British) certainly not:
Charlie shook his head vigorously. ‘Not on your nelly, mate.’
[originally as not on your Nelly Duff, rhyming slang for 'puff' (i.e. breath of life); modelled on the phrase not on your life]
Discuss word origins and meanings.
End of topic.