So it seems that what I was told was incorrect.
My own research has come up with a few explanations as to where it originated from, but all seem to agree that it's a derogatory term used by black people against white people. There are also different spellings of the term.
I find this odd as I could have sworn that the two neighbours in Love Thy Neighbour called each other black and white honkey
The two most common ones are that black people wanted something to use in response to being called a nigger and that the insult was used towards white men who went into black areas looking for prostitutes. They would honk their horns to summon a black prostitute that caught their eye, so any passing black men would call them "honkeys".