Green’s Dictionary of Slang

not a chance, absolutely impossible.

1958		F. Norman Bang To Rights 105: Now this is a real favour for which you would think he would be greatfull. But is he not on your Nellie.
1959		C. MacInnes Absolute Beginners 94: ‘Not on your Nelly, we won’t,’ [i.e. have twelve children] said Miriam.
1960		B. Kops Dream of Peter Mann Act I: peter: Playing chess? I’ll give you a game. alex: Not on your Nelly – I only play against myself.
1964		N.B. Harvey Any Old Dollars, Mister? 151: Me steal? Never in your nellie!
1966		(con. 1954) J. McGrath Events While Guarding the Bofors Gun I iii: What, do O’Rourke’s bash while he sits pouring Guiness down him, – not on your smelly nelly.
1967		J. Wynnum I’m a Jack, All Right 39: ‘Would you have taken it on if he had [i.e. told the truth]’ ‘Not on your Nelly!’.
1982		J. Sullivan ‘A Losing Streak’ Only Fools and Horses [TV script] Oh no, no, no, no, no, Del Boy. Not on your Nelly.
1989		H. Harrison Bill [...] on the Planet of Robot Slaves (1991) 150: ‘Wait til dark, then we bash them green meanies [...]’ ‘Not on your nelly!’.
1999		Guardian Weekend 13 Nov. 100: Not on your flipping Nelly.
2002		‘Barbara Vine’ Blood Doctor (2003) 187: We’ll still be able to come and eat and drink – won’t we? Not on your nelly, says Lachlan.
2004		J. McCourt ‘Vilja de Tanquay Exults’ in Queer Street 394: Oh, not that / He was in it, or anywhere near it, darling, / Not on your nellie.
2018		G. Gilmore Class Act [ebook] ‘[D]o you think I should call her?’ [...] ‘Nah, Davie, not on your nelly!