Emily Blunt - Biography - IMDb
Emily is very difficult to type as she's modest and a bit guarded when revealing personal facts, so this is not hard and fast by any means.
The interview above is more personal than others, where Emily opens up about her childhood and her abilities as an actress, which sheds some light on potential personality types, as does her quotes from her imdb bio. My gut says she's an INFP. She was shy as a child and would stammer, and enjoyed Introverted pursuits such as creative writing, playing the cello, and singing. She internalizes how she didn't fit in as a child and how she enjoyed analyzing people, which is an Intuitive Feeling function, more than a Sensing Thinking function. In most interviews she goes into detail about events (builds up) as opposed to talking about the big picture (boils down), which is a P function more so than a J function, and she also seems more game for a laugh and open to spontaneity like a Perceiver. J's or INFJ's are more closed with their(our) systems, and less up in the air. That's code for, 'She's not frustrated enough about life to be an INFJ'! However, she's difficult to read, a bit hidden even, but I will go with a soft IF as her dominant function and a soft EN as her secondary function. IF is noticeable in how gentle she is in her communication, but EN is noticeable in the rhythm of how she communicates; gentle bounces from topic to topic and back again.
Without this interview I would've pegged her as a dancer and a class clown, then gone with ESFP, and never known she's none of those things in real life. One of the big tell tale signs that she's an INFP from the interview was that she's terrible at driving!

ES tasks are sources of great embarrassment and laughter for INFP's, like Louie C.K. stuck in the Hudson with his boat!
This site says she's an INFP as well, however, I disagree with a lot of them on that site.