He trained at the Bristol Old Vic Theatre School, where his classmates included Richard Coyle and Oded Fehr.
Other television credits include Maisie Raine, Tipping the Velvet, ShakespeaRe-Told and The Worst Week of My Life.
In May, he appeared as Hedley, the landlord of the local pub in BBC drama The Invisibles, a story of two retired crooks returning to Britain from abroad.
He starred in Frequently Asked Questions About Time Travel a comedy sci-fi film with Chris O'Dowd, Marc Wootton and Anna Faris, ITV drama Married Single Other with Ralf Little and Miranda Raison, the BBC mini-series Cranford as a poor man struggling to feed his six children and wife, and in Robin Hood as Robin's father, Malcolm.
In 2002, he starred as Private Willie McNess in the major motion picture Deathwatch, a 2002 European horror film directed by Michael J. Bassett.
Empire had announced that Kelly would be voicing the role of John Lennon for the then-upcoming 3D remake of Yellow Submarine before the project was cancelled.