I might as well be the one to make this obvious and often-repeated point: British people have got hundreds of different accents. But of course, all accents have changed since the 18th century, some more than others. I disagree with the Reddit factoid that "the British accent has changed more than the American accent has". In the first place, it's a question of accents and not one accent, and in the second, clearly both accents in America and Britain have changed.

But it's clear that the more archaic accents and dialects in Britain represent an older form, and more resemble older forms of spoken English, than North American English, as one would expect. The most archaic accents and dialects of England are those that have retained their rhoticity, like the West Country, and some accents of Yorkshire, some older inhabitants of which even still use "thee" and "thou". The accents of Scotland and Ireland were always rhotic. Scots, which is the dialect of English spoken in Scotland, also retains some similarities with Old English pronunciations.

But I think RP is of more recent growth, originating from the middle classes in the home counties in perhaps the 18th century, and latterly being associated with the public schools and the ruling class.

This is also a good question for /r/linguistics.