Hugh was born Peter Dennis in 1962 in North London. His father was the Bishop of Saint Edmundsbury and Ipswich (John) between 1986 and 1992. He attended University College School in Hampstead (with writer Will Self), and then St. John's College, Cambridge, reading Geography. He met Steve Punt, his regular comedy partner, in the Cambridge Footlights, but went to work for Unilever for six years after graduation before they went full-time into comedy. Hugh has been married to Catherine (Kate) Abbot-Anderson, a sound engineer, since 1996, and they have two children, Freddy (b. 1997) and Meg (b. 1999).