Hepple graduated from the Royal Academy of Dramatic Art in 2006. The same year he made his professional debut in Alaska at the Royal Court Theatre with Rafe Spall and Christine Bottomley.
He then appeared in Burnt by the Sun alongside Ciarán Hinds, Rory Kinnear and Michelle Dockery at the Royal National Theatre.
In June 2009, Hepple appeared in Been So Long by Ché Walker, with music by Arthur Darvill, at the Young Vic.
He has appeared on stage in theatres across the United Kingdom including the You