Alfred Hitchcock is credited as saying he liked to cast well-known stars, such as Jimmy Stewart and Cary Grant, in his movies because it allowed him to skip two reels (about 20 minutes) of exposition. It makes sense - you don't need to explain who the character is because the audience already knows. You can just jump into the story.
That explains the casting of Anne Hathaway in One Day. She's immediately recognizable by movie goers and we only need a small bit of context to understand her character. We'll get to the part about a famous American playing a Scots lass in a moment. I don't understand why they cast an unknown as the male lead. Let me explain the movie first.
One Day is a visit to two friends on most July 15ths for two decades and only on July 15. Some days are good, some are bad. It was odd to not spend any substantive time with the characters; we just had to accept that they had lived the 364 previous days and that stuff happened without us. It's an interesting premise but probably better suited for the novel on which One Day was based.
One Day is a romantic drama. My problem is that the couple was a lousy match in 1988 and were even worse 15 years later, when they were both single at the same time. By the time their romance was blossoming, I stopped caring. The ending was also terrible. Please do not rush out to see One Day.
That male lead was a problem. While Hathaway is instantly familiar and certainly earned her keep by getting asses in seats during opening week, I didn't recognize the male lead from scene to scene. In fact, I wasn't sure which of the graduating class to keep an eye on at first. Then, as he changed his appearance every July 15, I had to wait until I knew for sure it was him before I started paying attention to what the characters were saying. Based on the first scene, I knew he would be one of these types: lovable rogue; redeemable bad boy; or asshat. He wasn't at all lovable or redeemable. Why should I spend 100 minutes watching a romantic movie with a guy I wouldn't like if I met him?
I saw a few stories about Anne Hathaway's English accept on the 'net last week. In fact, it was sometimes referred to as the worst English accent of all time. Not being English, I can't weigh in on the fine points, but I recognized that it was pretty good. It was good in Becoming Jane, as well. Thing is, it did change over the course of the movie, but I think that was intentional. She starts out as a Scots schoolgirl in some English hinterlands college. She then moves to London and gradually adopts a more sophisticated accent. Later, when she's successful in her career, her whole demeanor changes, clothes, accent, the works. I think Anne's accent worked just fine. If you want to pick on One Day, there is plenty to pick on, such as the lousy story or the lack of face time for Romola Garai, but lay off the accent.