Meaning of "garn" in My Fair Lady

At the beginning of the My Fair Lady movie, there is a monologue of prof. Higgins like this:

Hear a Yorkshireman, or worse
Hear a Cornishman converse
I'd rather hear a choir singing flat 
Chickens cackling in a barn 
Just like this one 
Garn!

My question is: what is the meaning of this "Garn"?

Garn is, as Prof. Lawler tells you, Shaw's orthographic approximation to Eliza's pronunciation of the phrase Go on!.

Go on, however, has little to do with the literal meaning of those words: it is a lower-class colloquial expression which dismisses what the previous speaker has just said as false, incredible, or absurd.

There are similar expressions which employ the notion of dismissing a speaker as a metonymy for dismissing the speaker's statement: Go to!, in Early Middle English, Get away! and Go way! in 19th century US speech, Get out and Gedahdahere in 20th-century US slang, Get off it in recent US slang. Other readers can no doubt provide more examples from recent British speech.

Why not ask Higgins himself?

ELIZA: Garn!

HIGGINS: "Garn"-I ask you, sir: what sort of word is that?

HIGGINS: It's "ow" and "garn" that keep her in her place,
Not her wretched clothes and dirty face.
Why can't the English teach their children how to speak?
This verbal class distinction, by now, should be antique.
If you spoke as she does, sir, instead of the way you do,
Why you might be selling flowers too.

Hooker, a Tolkien scholar, argues that "garn" is a "phonetic distortion" that should not make any sense:

It entirely misses the point that Garn! is a phonetic distortion that is marked for the social stratum to which the speaker belongs. In other words, it needs to be mispronounced and 'vulgar.' The context of the dialogue in My Fair Lady at the point that Eliza says Garn! is phonetics. Professor Higgins and Colonel Pickering are both phoneticians, and they are discussing pronunciation. The ideal translation of Garn!, therefore, should also be a phonetic distortion. In other words, it is the phonetic distortion that is the most important piece of information to convey in the translation of Garn! in this context, not the exact semantic value.

Citing the OED, Hooker notes its origin as a pronunciation of "go on!":

It is not particularly easy to find a translation for garn. The Oxford English Dictionary (OED) lists garn as an interjection, expressing "disbelief or ridicule of a statement." It is marked as colloquial usage, representing the--chiefly Cockney--pronunciation of go on! says the OED. This explanation of its origin, however, belies its stylistic marking. One of the examples in the OED indicates that its use is vulgar, and this is the marking that is given in the usually thorough Wildhagen German translating dictionary.4 The OED quotes the Glasgow Herald from 1925: "He complained that if he used such words as 'garn' or 'struth'5 he was accused of vulgarity ..."