If some apocalyptic event occurred, and there was no Internet, radio, TV,

[raccoon]

planes, ships that could cross the Atlantic, IOW no contact between the US and the UK, how long would it be before Americans and people from England couldn't understand each other and would be considered to be speaking different languages?

[Basileus Basileon]

1. Without any mass communication whatsoever? Like new Dark Ages?

Probably, oh, five hundred to a thousand years, depending on schooling, given the evolution of the Romance languages.

[ZombieNixon]

2. A couple hundred years, probably, to be considered different languages

a la English vs. Scots. A couple more hundred to be mutuall unintelligible, like English vs. Dutch.

Hell, if public schooling went the way of the dodo and only rich people could afford a full education, you could even begin to see a more significant diversion in the registers of the upper vs. the working class in a single area, approaching very different dialects (compare RP English with a dialect like Northumbrian).