So if the new you know who is British.. (SPOILER)

[7thsealord]

I'm more worried about why Carol Marcus is suddenly British. WHY?

How do we know the prime Carol Marcus wasn't British by birth?

Sure the nuCarol Marcus might have a British accent but as others have already said you can pick up a language by living in a country, so as I said above it's equally plausable that in the prime time line Carol was born in Britian but grew up in America.

It's never been stated onscreen where Carol Marcus was born. Just as San Fransico has Starfleet HQ, London might be where the Science HQ is.

Entirely reasonable. I would add that TWOK's Carol Marcus is twenty-plus years older. That is sufficient time (IMO) for someone to lose an accent either unconsciously (we all tend to mimic those around us) or deliberately.

Another less serious alternative, is that the later Carol was a victim of 'Foreign Accent Syndrome' ( http://en.wikipedia.org/wiki/Foreign_accent_syndrome ), which "reset" her British accent to North American.