He began his career as a stand-up comedian before playing the role of the inventor Archie in the children's television series Balamory.

[9] Jupp won So You Think You're Funny?, Leicester Mercury Comedian of the Year in 2001 and was a Perrier Award Best Newcomer nominee in 2003 for his show Gentlemen Prefer Brogues.

[11] He also had a role in the BBC Scotland comedy programme, Live Floor Show, where he played an eccentric, foul-mouthed comedian.

In 2007, Jupp appeared fleetingly in Harry Potter and the Order of the Phoenix as a television weatherman who complained about a hot drought.

Jupp appeared in Series 3 and 4 of the political comedy, The Thick of It, as John Duggan, an incompetent press officer with a habit of making inappropriate comments.

In January 2011, Jupp was a team member alongside Goldie and Phill Jupitus on the music quiz Never Mind The Buzzcocks.

In March 2012, he appeared in an episode of the televised 45th Anniversary series of BBC Radio 4's Just a Minute quiz show, alongside Paul Merton, Gyles Brandreth and Liza Tarbuck.

He was featured in the 2014 World War II film, The Monuments Men, as British officer Major Fielding.

In 2015, Jupp appeared as a team captain on The Really Welsh Christmas Quiz, alongside comedians Chris Corcoran, Elis James, and Omar Hamdi.

In 2018, Jupp made guest appearances as Basil, an incompetent lawyer, in the television drama by ITV The Durrells.

In 2011, he starred in the self-penned BBC Radio 4 comedy, In and Out of the Kitchen, "the diary, written for publication, of a somewhat minor celebrity chef, Damien Trench".

[18] He played the title character in BBC Radio 4 comedy Boswell's Lives (written by Jon Canter) which ran for four series, 2015–2018.

[21] In March 2008, Jupp performed his third solo show, Everyday Rage and Dinner Party Chit Chat, at the Etcetera Theatre in Camden.

[22][23] In 2019, Jupp played the role of actor David Tomlinson in The Life I Live, a one-man show at the Salisbury Playhouse and other theatres.