|The image is from the Hope Not Hate website.|
I'm convinced that it began to be used because the terms “fascist” or “Nazi” came to embarrass Leftists precisely because they accused almost everyone under the sun of being a “Nazi” or a “fascist”. Others got sick of it too. Thus, all of a sudden, the phrase “far right” came on the scene.
Thus the substitution of “Nazi” or “fascist” with “far right” is very much like the substitution of “capitalism” with “neoliberalism” during almost the same period. (Is this coincidental?) And, in both cases, I'm prepared to accept the there are conceptual and political differences. It's just that most users of “far right” and “neoliberalism” wouldn't be able to tell you what they are. Indeed if they could - or did - cite important and substantial differences between the Far Right and Nazis or fascists, the use of the phrase "far right" would loose its point and political efficacy.
To put this plainly, to the majority of Leftists (as well as to most regional journalist):
“far right” = Nazi/fascist.
Try and test Leftists (as well as journalists) out. Ask them to distinguish a member of the “far right” from a Nazi or a fascist. They won't be able to do so in most circumstances. (Leftists could, of course, offer superficial differences in order to prove a point.)
This isn't to say there can't be a Far Right that's not Nazi or fascist. I'm only commenting on the word as it's used by Leftists.