Yes and no. Depends on the region and what region we're comparing them to.
Cockney dialects sound a bit unrefined (though for the record I love that accent, one of my favorites to mimic), also British people say **** a lot more, and there isn't much refined about that.
On the other end they usually enunciate their words more clearly (I'm not sure which region it is that has that more refined tone, now that I think about it... hmm...), and also since they use the u's in various words (colour, flavour) it sounds a bit more sounded out. This is what I'd point to on the "they sound more refined end"
That said, anyone sounds more refined than the terrible deep south accent large numbers of Americans use.
That also said, rock whatever you have and don't feel ashamed or shy about your accent, in no way does it actually make you any more or less refined. The human voice and it's cadence and inflection make it so throughly unique that one can make it out with more clarity and accuracy than a face or body when identifying that person, so be proud of your unique style, whatever that may be.