Act 1, Eliza's remark when Higgins boasts that he can place one within two miles in London, or even two streets.
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The irony is more situational rather than verbal. I think the irony lies in the fact that the Note Taker sees himself as an aficionado of character and the flower girl, low on the social scale, calls him on it.
I wouldn't call it irony so much. She calls his character into question. In that context she is perfectly right. The guy is a jerk.