This is simply nonsense.
That the current accent is driven by a particular fad aimed at highlighting upper class status doesn't imply that class distinctions are novel, just the particular effort to demarcate them (which wasn't durable, obviously, as RP isn't exclusive to the upper classes.)
No one, AFAICT, did that. The reference to “modern British English” is not, as I read it, a reference to “the current diversity of British accents”, but rather “the current dominant British accent”.
Fair point - I would also agree that the idea of a "dominant" British accent seems a bit odd - certainly not in terms of what people actually sound like (rather than the broadcast media).
In a highly class-conscious society where the vast majority of people spoke English as their first language, it seems fairly unlikely that accent would have had no connotation of social status.
It thus seems hard to believe that the development of the modern diversity of English dialects would have been spurred by some sudden need to mark class distinctions.