[4] Rigby has worked as a stand-up comedian, having appeared at the Latitude Festival, won the 2007 Laughing Horse New Act of the Year, and been a nominee for winner of the 2007 So You Think You're Funny competition.
[6] From 2011 until 2014, Rigby voiced[7] Copenhagen in three series of the BBC Radio 4 comedy Warhorses of Letters alongside Stephen Fry.
He performed in Tom Basden's Holes at the Arcola Theatre in London from July to August 2014 alongside Mathew Baynton.
[9] In 2019, he voiced the title role in the BBC Radio 4 sitcom ReincarNathan, alongside Diane Morgan and Josh Widdicombe.
[11] In 2022 and 2023, Rigby starred as The Maniac in Tom Basden's adaptation of Dario Fo's Accidental Death of an Anarchist with runs in Sheffield and London.