He abandoned completion of his thesis to pursue a career in comedy. Miller’s interest in comedy began when a friend asked him to help ferry around the judges of the National Student Drama Festival, which was being held that year in Cambridge. Having already finished his undergraduate degree, he joined the Footlights in 1989, working with Andy Parsons, David Wolstencroft and Sue Perkins, and went on to direct a revue.

Miller moved to London to pursue a career in comedy. He was introduced to fellow Cambridge graduate Alexander Armstrong in 1992, at the TBA Sketch Comedy Group, a comedy club which ran at the Gate Theatre Studio, Notting Hill throughout the 1990s. They performed their first full-length show together at the Edinburgh Fringe in 1994 and returned in 1996, when they were nominated for the Perrier Comedy Award.

Their success resulted in the commission of the television series Armstrong and Miller, which ran for four series from 1997 to 2001 – one on the Paramount Comedy Channel and three on Channel 4. In 1998, the duo also had their own radio show with the same name on BBC Radio 4, which featured many of the sketches and characters from their TV series. After a six-year break, the show was recommissioned for Hat Trick Productions as The Armstrong & Miller Show and three series have been produced. In 2008, they also had a second radio show, Children’s Hour with Armstrong and Miller.

Miller was awarded a Judges’ Commendation for his portrayal of Hamlet at the 1990 National Student Drama Festival. He co-wrote MindGym, winner of the first BAFTA Interactive Entertainment Award for comedy in 1998, with Tim Wright and Adam Gee. He and Armstrong won a BCA Award for The Armstrong and Miller Show. In 2010 they also won a BAFTA for The Armstrong and Miller Show.

Miller also started acting in films, starring in Steve Coogan’s first feature film, The Parole Officer (2001). In 2003 he played the role of ‘Bough’, sidekick to Rowan Atkinson’s title character, in the film Johnny English. In 2004 he co-starred in The Prince and Me.

In 2004 and 2005, he starred in two series of the BBC television series The Worst Week of My Life, with Sarah Alexander. In 2006 he took part in a three-part Christmas special, The Worst Christmas of My Life. He starred as James Peregrine Lester in ITV’s 2007 sci-fi drama Primeval and as Mr Jonathan in the Australian film Razzle Dazzle: A Journey into Dance.

Miller’s first wife was Belinda Stewart-Wilson, who guest-starred with him in Series 3 of Primeval. The pair, who have a son born in 2006, divorced in 2011. Miller has another son, born in late 2011, and a daughter, born in June 2015, with his second wife, production executive Jessica Parker, whom he married in September 2013; Jessica is the daughter of British musician Alan Parker.

Miller provided the voice for the ITV Digital and now PG Tips Monkey in a popular series of television advertisements featuring Johnny Vegas. In 2008, he appeared as television producer Jonathan Pope in Tony Jordan’s series Moving Wallpaper on ITV1 and starred in Thank God You’re Here. In 2010, he made his directorial debut with the film Huge.

On 20 February 2009, Miller appeared with Rob Brydon in an episode of QI (Series 6. 9). The two have often been mistaken for each other, and as a joke they dressed in similar shirts for the episode and shared an on-screen kiss. Miller plays the guitar and drums.

In January 2011 he presented an episode of the BBC science series Horizon titled “What is One Degree?”. Later in 2011 he reprised his role as James Lester in the TV series Primeval. From November 2011 he played the role of Louis Harvey in The Ladykillers at the Gielgud Theatre.

From 2011 until the series three premiere in 2014, Miller starred in the BBC-French co-produced series Death in Paradise as Detective Inspector (DI) Richard Poole. A third series of Death in Paradise was commissioned for early 2014. On 9 April 2013 it was announced that Miller would be departing the series, to be replaced by actor Kris Marshall. Filming began in March 2013, and Miller left in May after completion of the first episode, in which his character was murdered.

On 23 July 2012, Miller began touring for his book, It’s Not Rocket Science, from the Royal Society in London. He also appeared at the British Comedy Awards with Armstrong on Channel 4. In 2013, Miller took part in an episode of Room 101 and a Comic Relief special of game show Pointless. On 13 December 2014, he appeared in a Christmas edition of The Celebrity Chase.

In 2014, Miller appeared in the feature film Molly Moon and the Incredible Book of Hypnotism. He also appeared with Billy Connolly and David Tennant in the film What We Did on Our Holiday.

On 6 September 2014, Miller guest starred in Doctor Who as the Sheriff of Nottingham in the third episode: “Robot of Sherwood”.

In 2015, following the 800th anniversary of the Magna Carta, Miller starred as King John in Series 6 of Horrible Histories.

Since October 2015, Miller along with Ruth Jones and Will Close, appears in adverts for British supermarket Tesco as Roger with Jones as his wife Jo and Close as their son Freddie. In 2016, Miller co-presented the ITV entertainment series It’s Not Rocket Science alongside Rachel Riley and Romesh Ranganathan.

In February 2016 Miller issued a book, accompanied by a lecture tour, entitled The Aliens are Coming!, examining the question “are we alone in the universe?”

Miller played the role of Murray in the six-part BBC sitcom I Want My Wife Back, starring alongside Caroline Catz. In 2016 he appeared in the Channel 4 comedy Power Monkeys.

In 2018 he returned to the role of ‘Bough’, sidekick again to Rowan Atkinson’s title character, in the film Johnny English Strikes Again. In September of that same year he played the role of Wolf Hall on the BBC sitcom Upstart Crow.