When did the British and the Americans start to pronounce "o" (as in "God") differently?
Was it due to changes in America or England?
The change in the vowel phoneme used in "God" certainly occured in American, not British, accents. One piece of evidence indicating this is that in a usual American English accent, the vowel of "God" has merged with the vowel of "father," while this is not so for a usual British English accent. The spelling provides a clue that the distinction in British English is due to retention of an original distinction rather than due to an innovative split.
Wikipedia, which is not such a reliable source but which is the best I have right now, says the change happened "from the 18th century on."
The general development of the "short o" sound goes like this:
In a usual accent from the south of England, the vowel in "God" currently tends to be somewhere around [ɔ], although often transcribed /ɒ/ due to tradition. It contrasts with both [ɑː], in "father," and [oː], in "laud."
In a usual Scottish English accent (not the same thing as Scots or Scottish Gaelic), the vowel in "God" is traditionally transcribed as /ɔ/, and it is merged with the vowel of "laud" but not with the /ɑ/ of "father."
In a usual "general" American English accent, the vowel in "God" is [ɑ], merged with the "father" vowel; in American English affected by the "Northern Cities Vowel Shift" it has been fronted to more or less [a]. In accents with the caught-cot merger "laud" has this same vowel; in accents without the merger "laud" has a distinct vowel usually transcribed /ɔ/, but often phonetically closer to something like [ɒ].
American English is not really so much more conservative than British English. Other innnovative phonological/phonetic elements that are more common in North American English than in British English are:
These are not universally present in American English accents, and yod-dropping and t-lenition exist in some British English accents as well, but these innovations are certainly more common in North American English than in British English.
In Britain, the "o" vowel, [ɒ], in words like dog, hod, pot, is pronounced with rounded lips and the tongue back in the mouth. Americans do not have this vowel, instead pronouncing the same words using the "ah" vowel, [ɑ], with the lips unrounded and the tongue back but more relaxed. This is the same vowel in card or bard. In some cases in the US the "o" is pronounced using the "or" vowel in words like long (Central East Coast) and horrid (especially in the western US).
The "plummy" quality of some RP speakers is probably due to an exaggeration of this "o" vowel, and other vowels, by pushing the tongue as far back as possible, accomplished by speaking whilst imagining a mouth full of plums.
Long vowels in Middle English were pronounced as they were in Latin but, during the 15th and 16th centuries, they changed to what we have in general today. This change is called the Great Vowel Shift. In major cities around the Great Lakes area, linguists have noted since the 1970s what they call the Northern Cities Chain Shift. On the West Coast you hear many vowel shifts, notably in younger people, and sometimes words are spelled to match (sense → since, pen → pin). My daughter growing up pronounced it MickDonalds.
- hot (haht) → hat
After American–British split, up to the 20th century: (This period is estimated to be c. AD 1725–1900.)
The father–bother merger: /ɒ/ as in lot, bother merges with /ɑ/ as in father, so that most North American dialects only have the vowel /ɑ/.
Exceptions are accents in Eastern New England, such as the Boston accent, and New York City.
The difference between the majority of accents is due to vowel rotation. Meaning that in point of fact a typical British accent (and there are of course many) will sound all five vowels differently to an American accent. This is true for all accents.
If you want to hear this in action, do you best English accent and your best American and say a sentence like 'Harry is in Paris.' Then say 'Henry is in Hendon.' And so on for all vowels. If you have an ear for accents you will find all of the vowels sounds are different. This is chiefly what distinguishes accents.
With regard to when the changes occurred, surely it would have been gradual, as the English language speakers became separated by distance and immigrants poured into America. Each arriving group would have brought their own influence to bear on pronunciation. To my ears many American words, including 'God' and 'arse/ass' for that matter, have an Irish sound and they turned up in large numbers after the Irish famine of the 1840s.