Coulson was born in Manchester, and attended Westminster School in London on an academic scholarship. He was a member of the UK's National Youth Music Theatre from 1990–1997, and went on to the University of Cambridge, where he received a degree in English from Clare College in 2000. While at university, he played the M.C. (Master of Ceremonies) in Cabaret, Arturo Ui in The Resistible Rise of Arturo Ui and Claire in The Maids, as well as appearing in film and television.