Natalie Wolchover explains that it is the "standard British accent that has drastically changed in the past two centuries, while the typical American accent has changed only subtly":
Traditional English, whether spoken in the British Isles or the American colonies, was largely "rhotic." Rhotic speakers pronounce the "R" sound in such words as "hard" and "winter," while non-rhotic speakers do not. Today, however, non-rhotic speech is common throughout most of Britain. For example, most modern Brits would tell you it's been a "hahd wintuh." It was around the time of the American Revolution that non-rhotic speech came into use among the upper class in southern England, in and around London. According to John Algeo in "The Cambridge History of the English Language," this shift occurred because people of low birth rank who had become wealthy during the Industrial Revolution were seeking ways to distinguish themselves from other commoners; they cultivated the prestigious non-rhotic pronunciation in order to demonstrate their new upper-class status.
The Dish 