Cox was born in Vienna to a British father and an Irish mother. Her parents later divorced. Both are pianists, who had originally come to Vienna on a grant for musicians. Cox grew up in Vienna and finished school in 2003. She became interested in acting after taking part in a play as part of her English lessons in her final year. After finishing school she enrolled to study acting at the Max Reinhardt Seminar.

In 2008 she was a contracted theatre actress at the Theater in der Josefstadt in Vienna. In 2011 Cox moved to Berlin, and since then she has appeared in various films and series on German and Austrian television, among them several Tatort films. Since 2015 she has played the Viking woman Brida in the television series The Last Kingdom, which made her known to an international audience.