As for the “why,” though, one big factor in the divergence of the accents is rhotacism. The General American accent is rhotic and speakers pronounce the r in words such as hard. The BBC-type British accent is non-rhotic, and speakers don’t pronounce the r, leaving hard sounding more like hahd. Before and during the American Revolution, the English, both in England and in the colonies, mostly spoke with a rhotic accent. We don’t know much more about said accent, though. Various claims about the accents of the Appalachian Mountains, the Outer Banks, the Tidewater region and Virginia’s Tangier Island sounding like an uncorrupted Elizabethan-era English accent have been busted as myths by linguists.
Around the turn of the 18th 19th century, not long after the revolution, non-rhotic speech took off in southern England, especially among the upper and upper-middle classes. It was a signifier of class and status. This posh accent was standardized as Received Pronunciation and taught widely by pronunciation tutors to people who wanted to learn to speak fashionably. Because the Received Pronunciation accent was regionally “neutral” and easy to understand, it spread across England and the empire through the armed forces, the civil service and, later, the BBC.
I had to look this up and now my mind is blown.