I'd just add that there is no such thing as a 'British accent'. There are a multitude of accents and dialects spoken all over the UK. What you are probably referring to is '
received pronunciation,' which is what British newsreaders primarily used to sound authoritative.
It should be noted from the wiki page that hardly any actual British people speak with RP, and people using it are generally thought of as posh.
Major accents in the UK include cockney (mostly east London and parts of essex), estuary english (kent, essex, london), scouse (Liverpool), manc (Manchester), black country (I should note 'Black Country' refers to a region in the UK around Birmingham/Wolverhampton, so named due to it's blacksmithing heritage), West country (Bristol down to cornwall - think pirates), Scots, Welsh, Northern Irish (and even within Scotland and Wales the northerners' accent sounds quite different from the southerners' accent), geordie (Newcastle/Durham), Yorkshire etc and so on. There are also weird pockets of accents - the natives of Corby, which is a small town in the south midlands, sound fairly scottish - this happened because factory owners of the town shipped a load of Scots down for cheap labor a few generations ago and the accents blended.
As for your question - i really don't mind, although it can be disconcerting to hear somebody using received pronunciation in everyday speak - it sounds artificial in itself.