I don't know about the U.K. In the town I live in, in the United States, near Boston, people who grew up in town indeed use a vowel sound like the "o" in "not" in words like "laugh," "bath," and "aunt." I say them like the "a" in "bad" or "cat."
I pronounce the words "aunt" and "ant" exactly the same way; they do not. They say "ant" the same way I do, but they say something like "ont" for their mother's sister.
The local pronunciation is not upper-class, it's just the local pronunciation; and it is almost certainly Irish, not Boston Brahmin.
P.S. The "Dictionary of American Regional English," which documents this kind of difference, is 5,544 pages long and is published in five volumes!