Raised in Tufnell Park and Crouch End, North London, Alwyn is the son of a psychotherapist mother and a documentary filmmaker father. He was educated at the City of London School. Although an "introverted" child, he secretly wanted to be an actor. He became a member of the National Youth Theatre in his late teens. While studying English literature and drama at the University of Bristol, he acted in two student productions at the Edinburgh Fringe Festival. After graduating in 2012, he completed a BA in acting at the Royal Central School of Speech & Drama.