Green’s Dictionary of Slang

not likely phr.

a phr. implying absolute reluctance, ‘in no way will I do that’; usu. in excls. below.

G.B. Shaw Widowers’ Houses II iv 47: Catch him going down to collect his own rents! Not likely!
[UK]Breton & Bevir Adventures of Mrs. May 19: An ’usband oughter be a combination nurse-cook, and a nice devoted chap [...] But is ’e? Not likely!
[UK]A. Sillitoe ‘The Fishing-Boat Picture’ Loneliness of the Long-Distance Runner (1960) 73: What was I going to do? Knock him flat and drag Kathy back by the hair? Not likely.
[US]M. Braly Shake Him Till He Rattles (1964) 22: ‘You holding?’ ‘Not likely.’.

In exclamations

not bloody likely! [popularized by George Bernard Shaw’s Pygmalion (1913), in which the Cockney flowergirl Eliza Doolittle shocked audiences with her then taboo excl. ‘Not bloody likely!’]

an emphatic negative.

G.B. Shaw Pygmalion Act III: Walk! Not bloody likely. I am going to take a taxi.
[Aus]S. Gore Holy Smoke 31: ‘Not bloody likely!’ barks Dave.
[UK]P. Theroux Family Arsenal 79: Not bloody likely.
not fucking likely! [fucking adj. (4)]

an emphatic negative.

J. Osborne ‘Sport & Nationalism’, part of the Crossing the Borders Workshop 14 Aug. Royalcourtheatre.com 🌐 ‘He had an open chance, I could’ve got it in from there.’ ‘Not fucking likely, your random ’eaders’ll go anywhere but in the net.’.
not Pygmalion likely! [for ety. see above]

a euph. for not bloody likely! excl.

[Scot]B. Stuart Far To Go 145: If I had offered him a pork chop, he could not have kicked up more row. Walk into Beni Abbes?—not pygmalion likely!
R.G. Hay Clarice Ch. 8C 🌐 ‘Next time you three can come along, too. And we can play a sort of scissors, paper, rock game.’ Arthur seemed to quickly run through the possibilities in his head. ‘Not Pygmalion likely’ he said. ‘I couldn’t win, and Jane couldn’t lose.’.