By plain "r" sound, I meant "r" when it appears at the beginning of a word - such as "rush" or "ring" or when combined with another consonant(s) in the middle of a word, like "scrape" or"anthrax". To my non-professional ear, American English and southern British English use an identical sound here, even if the vowel sounds are somewhat different. I wasn't referring to RP, which - as many have pointed out (Nona especially!) - is an increasingly rare form of English, but rather, the English as spoken in the south east of the country. I take it one of the ways of pronouncing "r" in RP to which you refer is with a "trill" (ie, vibrating the tip of the tongue behind the upper teeth). Amongst southern English speakers, this is a sound I have only ever heard in pre 1960 movies!