This is obviously the text version of the Channel 5 story, so I have not heard the voices of the people involved. What I do know is that the terminology is way off. This is not "voice discrimination", this possibly is racism based on the sound of voice. Voice discrimination is something that people with speech problems would face. As a person with a speech impediment, I can attest that such a thing exists, but is not considered significant in society. Calling this voice discrimination is misleading. It is race or ethnic discrimination based on the voice, not discrimination because of the voice. A fine line to some, but not from my perspective.
In this case the problem I have is the distinction of why these people were allegedly denied housing. Were they denied housing because the landlord thought they sounded "black" or other minority, or were they denied housing because their speech indicated a lack of education or ignorance and thus considered a less desirable tenet? Again, I did not hear these people speak, so I don't know how they might sound. It may be bigoted to deny someone a house because they are not educated, but I don't think it is illegal.