I'm now wondering where I have heard "Use your inside voice dear!"
It could have been Hyacinth. I think inside voice is a good way of putting it anyway, not that I have ever used the term myself. I may do if I was a teacher though 
The poster a while back who described a delightful old man who always had something to talk about and treated everyone the same is definitely how I see someone of class. They do say that how someone treats the waitress is a good indicator of how nice a person they are and this definitely lines up with that.
Good breeding is classless because there are some "posh" people who have been well bred and know how to treat others well regardless of their station in life. Whether they are moneyed or their family was, the breeding which they have recieved stands them in good stead to be a decent citizen, not an asshole. Being philanthropic comes easy to them, often.
Meanwhile there are fake-posh people who treat the waitress badly and are general assholes, boast about their "wealth", ignore anyone them deem as beneath them and are insecure enough to have to name drop about who they mix with and where they shop , be seen at the right places, let everyone know what they have bought. These are tiresome people!
Posh is not an accent. Anyone can have elecution. It means nothing and even the news readers do not have elecution anymore.