Not on your Nelly
A British English expression, usually in the form of an exclamation that means 'not likely' or 'not on your life'. Eric Partridge maintains the origin dates from the 1930s and is from rhyming slang - not on your Nelly Duff/puff. Puff is slang for life, as in breath of life, hence 'not on your life'. Nelly Duff seems to be a purely fictitious character who has lent herself to the rhyming slang.