A few important points to address first:

1. The stereotypical English accent is just one of hundreds of accents of English as spoken in the UK.

2. The accent people in England have today is not at all the accent they had in the 1700s, regardless of which of the English accents you're looking at

3. Likewise, the "American accent" (again, there are many different ones) and the "Australian accent" (yup, many different ones of those too) were not what they are today.

All of the accents we have today are different than the accents of the people who lived in the exact same area 100 years ago. Accents are in a constant state of flux, and always have been.

The answer to "when" is "immediately", and noticeably within a single generation.

The answer to "what caused it" is migrations, contact with others, and of course the nature of language as a constantly changing thing.

You might also be interested in a few times this has been asked in the past, taken from the FAQ:

• Would Americans at the time of the revolution have spoken with a distinct non-British accent?

• When did the current dialect of American English diverge from traditional British English?

• When did Americans lose their Brittish accent?

• Differences in American and British English accents

• At what point in time did Americans develop an American accent (or accents, for say the north and south)?