Though I hope its been pointed out before, There is no such thing as a British accent, no more than there is a "European" one. Britain, like Europe, is a collection of countries with recognizably different accents.
It does get on my tits when people (usually Americans) equate "British" to "English", and then equate "the english accent" to either Victorian-esque, chimney sweep cockney or a poor impersonation of the Royal family (that is, the real Royal Family, not the sitcom)
Honestly I don't think that a posh accent makes you sound sophisticated, I think it makes you sound like a Spoiled shit. There's something to be said about a neutral-English accent but that, again, is different to "Posh" or "Upper class".
MOST English accents make you sound like a fucking idiot, Scottish accents make you sound angry (and gloriously so) whilst Welsh accents make you sound placid and confused, like a lost dog.