Dyson was born in Leeds, Yorkshire, England, son of Elaine Saville and Melvin Dyson. He has one older brother, Andrew Dyson, and a younger sister, Jayne Dyson. He was educated at Leeds Grammar School, now The Grammar School at Leeds. He studied Philosophy at the University of Leeds and later completed an MA in screenwriting at the Northern School of Film and Television. He lived in Highbury, London, but now lives in Ilkley, West Yorkshire.
Dyson is best known as co-creator of the hit West End play Ghost Stories, and as a member of the sketch comedy team The League of Gentlemen, along with fellow performers Mark Gatiss, Steve Pemberton, and Reece Shearsmith, all of whom he met while they were studying at Bretton Hall drama school.
The League of Gentlemen initially began as a stage act in 1995, which then was transferred to BBC Radio 4 in 1997 as On the Town with the League of Gentlemen, and then became a television series on BBC Two in 1999. The latter saw Dyson and his colleagues awarded a British Academy Television Award, a Royal Television Society Award, and the prestigious Golden Rose of Montreux.
Dyson has written several books including Bright Darkness: Lost Art of the Supernatural Horror Film, a non-fiction guide to horror films, and two collections of short stories entitled Never Trust a Rabbit – short-listed for the Macmillan Silver Pen award – and The Cranes That Build The Cranes which won the 2010 Edge Hill award. His novel What Happens Now was published on 6 April 2006 to favourable reviews and was nominated for the Goss first novel award.
He has co-created (with Simon Ashdown) the BAFTA nominated television series Funland, which aired on BBC Three, and wrote the Billy Goats Gruff episode of the BBC's 2008 series Fairy Tales.
He has worked as script editor and writer on BBC1’s BAFTA award-winning The Armstrong and Miller Show (2007–2010), where he created the licentious Flanders & Swann parodying Brabbins & Fyffe, accident prone historian Dennis Lincoln Park, disapproving lingerie saleswomen Lisa & Yvonne and the ‘Kill Them’ sketches amongst others.
He was the script editor of BBC Two sitcom Grandma's House (2010), BBC Three's Dead Boss (2012) and Walking and Talking (2012) for Sky Atlantic.
Due to Dyson's self-confessed lack of acting skills, he does not appear in The League of Gentlemen television series or any of its offshoots, apart from very brief cameos. He worked as the assistant producer instead. In the film adaptation he is played by Michael Sheen, although Dyson appears in the background of a few scenes.
Dyson has an interest in the supernatural fiction of English writer Robert Aickman and has adapted Aickman's work in a number of media.
Alongside his writing work, Dyson plays keyboards in a pop band called Rudolf Rocker, and has previously been a member of Leeds band Flowers for Agatha in the 1980s.
He is a patron of the charity No Panic.
With Andy Nyman, he co-wrote and co-directed the supernatural-themed stage production Ghost Stories. The play broke box office records at the Liverpool Playhouse and Lyric Hammersmith theatres where had its first run between February and April 2010 and transferred to the Duke of York's Theatre in the West End in June 2010 where it ran for thirteen months. In January 2011, he returned to the Lyric Hammersmith with Roald Dahl's Twisted Tales, the first stage adaptation of Roald Dahl's short stories Tales of the Unexpected.
Dyson was script editor on the BBC Two comedy-thriller The Wrong Mans written by James Corden, Mathew Baynton and Tom Basden. The show is about a pair of lowly office workers who become unwittingly embroiled in a deadly criminal conspiracy. Its first series was broadcast in 2013.
He writes and acts as script supervisor for the BBC sketch comedy series Tracey Ullman's Show starring actress-comedian, Tracey Ullman.