Born in Cambridgeshire, UK, Morris' parents are both doctors. He was educated at Stonyhurst College, a Roman Catholic boys boarding school in Lancashire, and then at Bristol University.
On graduating, Morris took up a traineeship with Radio Cambridgeshire, where he took advantage of the free access to editing and recording equipment to create elaborate spoofs and parodies. On leaving Radio Cambridgeshire, he worked at Radio Bristol, and Greater London Radio (GLR). Both stations fired him for on-air pranks.
In 1989, Morris gave up work as a mainstream disc-jockey, and devoted himself wholly to comedy with his next radio project, On the Hour. Working with Armando Iannucci, Patrick Marber, Richard Herring, Stewart Lee, Steve Coogan and others, he created a highly original spoof news show which was broadcast on BBC Radio 4. In 1992, a television version of On the Hour was commissioned by the BBC and it was broadcast under the name The Day Today. So convincing was the artifice of this current affairs parody that many viewers complained to the BBC. Morris characteristically dismissed their protests as 'boneheaded'. The Day Today made a star of Morris, and helped to launch the careers of Patrick Marber and Steve Coogan.
The 'sick comedy' which had bubbled under in On the Hour and The Day Today found full release, however, with Brass Eye, another spoof current affairs documentary show, this time shown on Channel 4. The station remit allowed for more shocking material, and Morris took full advantage of this freedom, exploring such taboos as infant mortality, incest, buggery, rape, suicide, sadomasochism, and more. A recent (2001) one off reprise of the Brass Eye format on the subject of paedophilia led to record numbers of viewer complaints, and a great deal of hysterical discussion in the press. Many complainers (a large number of whom appeared not to have actually seen the show, and freely admitted this) were confused as to Morris' intentions, and felt the satire was directed at the victims of paedophilia. In fact the satire was directed firmly at media coverage of paedophilia, something that was abundantly clear on actually watching the show.
Other projects since Brass Eye have included Blue Jam, an ambient late-night music and sketch show broadcast on BBC Radio 1, and a TV adaptation of Blue Jam called Jam.
In 2002, Morris ventured into film with the short My Wrongs 8245 - 8249 and 117, a version of Blue Jam sketch about a man looking after a sinister talking dog. It was the first film project of Warp Films, a branch of Warp Records. In 2003, this won the BAFTA for best short film.
Morris is notoriously reluctant to discuss his work, and his refusal to defend his morally ambiguous handling of sensitive subjects has added to the controversy surrounding it.