In addition to stand-up, Addison played Ollie Reeder in the BBC Two satire series "The Thick of It" and Toby Wright in its spin-off film "In the Loop", starred in the Sky Living comedy-drama "Trying Again" and appeared in three episodes of series 8 of "Doctor Who". He also co-created and starred in the BBC Two sitcom "Lab Rats". On radio, he previously hosted the weekly comedy news satire show "7 Day Sunday" on BBC Radio 5 Live from 2009 to 2010. In 2020, he co-created the FX parental comedy series "Breeders" starring Martin Freeman.