Sure. Posh. "Irritatingly nasal."
Sorry, does it mean something else in the UK?
In the UK there are very distinct accents which not only reflect where you were born and raised, but also your social status (in theory of course). Therefore to have a posh accent is actually a very specific set of accents, with specific vowels etc. It is rather remarkable how many different accents there are in such a tiny island.
There was a time in the UK when in order to make it as an actor you had to change your accent to the more acceptable "received pronunciation" which was a more high class accent - basically that typical "british accent" that people associate in general with brits. These days it is becoming much more popular to speak with the accent you were raised with. Though stereotypes still abound (think the same in the states with southern accents vs northern accents, or in Canada - eastcoast vs westcoast).
Many North Americans will lump virtually all british accents together as posh, simply because they are british (though we exclude cockney, because we've seen it as low class in a lot of films). But that is not the case in actuality in the UK.
Posh means exactly the same thing in the UK as it does in North America, it's just that a posh accent is very different depending on what your ear has become accustomed to. I am always so surprised by how people from the UK can distinguish so well between different accents down to the minutest of differences.