An Englishman's way of speaking absolutely classifies him.
The moment he talks he makes some other Englishman despise him.If you spoke as she does, sir,
Instead of the way you do,
Why, you might be selling flowers, too!
Those are probably my two favorite lines in my favorite song of my favorite musical, My Fair Lady. I have to admit I've been caught quoting them once or twice when asked by friends or family why I tend to be exacting about proper English speech. The movie made huge impression on me since I first watched it at age 6; Henry Higgins is kind of a personal hero of mine.
But how true are his words to reality today? Now, I've read all about Received Pronunciation, and hypercorrective hs, and they are indeed interesting topics to discuss, but I get the impression that not even the upper-class adhere to Received Pronunciation anymore, and that much effort has been invested by many British to be more colloquial in speech so as not to seem outwardly too posh or upper-class. I get the impression that many view speech distinctions as something to be publicly denounced or abhorred. That doesn't mean that those distinctions don't exist of course, but Received Pronunciation in particular seems to me a social distinction of a long past age, and besides there are a ton of other English accents to talk about. Discussing RP as the totality of what it is to be said on the subject also seems myopically centered on London to detriment of the rest of the UK.
I think it's also important to consider that the demographics of the classes and thus the linguistic baggage different ethnic groups brought into British speech might have changed the different distinctions. For example, I know that upper-caste Indians have become a prosperous group in the UK; have they in any way changed the markings of the upper class speech? What about the ascendance of Jews escaping from the Holocaust, and a "Yiddish" manner of speaking they might have brought with them? Have wealthy and prominent Russian moguls changed speech patterns? (For example, in this question the question-answerer remarks on the middle class' willingness to use na zdrovyeh as a toast in place of cheers; have other things changed?)
The converse probably holds too: I'd guess that immigrants from Commonwealth Carribean countries and Polish migrant workers have possibly changed distinctions on what it means to have "working-class" speech patterns. What can be broadly said about all this?
TL; DR summary: What examples can you offer of accents or speech differentiating social classes in the present day that doesn't discuss Received Pronunciation?
Best Answer
Things have certainly changed in that, for example, you find more TV presenters with regional English accents in more "serious" roles on national UK television. On the other hand, national news programmes still tend to be fronted by presenters with what are perceived as essentially "standard" English accents. Perhaps tellingly, it's been for some time common for national presenters to have Scottish, Welsh or Irish accents, but not regional English accents.
Figures in the public eye with notable regional accents such as John Prescott and William Hague have visibly attempted (with varying degrees of success and ridicule) to "iron out" (i.e. move more towards something like RP) their accent when speaking publicly. It's not clear to what degree this is conscious or subconscious, but either way, it's telling of our perception to accents that they do so.
Note that what is perceived as a "standard, non-regional" accent of English is almost certainly no longer RP as traditionally transcribed in EFL textbooks (assuming the principle of transcribing vowel sounds with the nearest cardinal vowel symbol). For example, the fronting of the /u/ vowel (so that it sounds closer to French "i" or "u" vowels)-- a phenomenon that is probably at least a century old-- now seems to be fairly standard, but is practically never reflected in general transcriptions in dictionaries, EFL textbooks etc.
It's worth considering that the British notion of "class" has probably changed somewhat in the last few decades as well. We live in a world where athletes are given knighthoods and Floella Benjamin is a baroness.