^We were shown that Admiral Marcus worked for Section 31, which had an office in London. It's simple to assume he thus lived in England when his daughter was born and raised. Clearly the Prime universe's Marcus family did not live in England. Carol was born after the timeline split, so there's no reason she couldn't have had a different upbringing from day one. After all, this Carol is in Starfleet while Carol Prime is a civilian. So clearly her life is different.
The real-world reason is that, although the filmmakers tested Eve with an American accent, they decided to go with her natural accent because they felt it helped sell her as a scientist. To Americans, English accent = smart.