Jones was born in Colwyn Bay, Wales. He was educated at the Royal Grammar School in Guildford, where he was head boy; he graduated in English at St Edmund Hall, Oxford. While there he performed comedy with Michael Palin, among others, in The Oxford Revue.

Jones appeared in Twice a Fortnight with Palin, Graeme Garden, Bill Oddie and Jonathan Lynn, as well as in The Complete and Utter History of Britain. He also appeared in Do Not Adjust Your Set with Palin, Eric Idle and David Jason (Jones speaks about this series during an interview which appears on both the DVDs for Do Not Adjust Your Set and the At Last the 1948 Show). He wrote for The Frost Report and several other of David Frost's programmes on British television.

As a member of the Monty Python troupe, Jones is remembered for his roles as middle-aged women and the bowler-hatted "man in the street". He typically wrote sketches in partnership with Palin.

One of Jones's early concerns was devising a fresh format for the Python TV shows, and it was largely Jones who developed the stream-of-consciousness style which abandoned punchlines and instead encouraged the fluid movement of one sketch to another - allowing the team's conceptual humour the space to “breathe”.

Jones also objected to TV directors’ use of sped-up film, over-emphatic music, and static camera style, and took a keen interest in the direction of the shows. He later committed himself to directing the Python films Monty Python and the Holy Grail, The Life of Brian, and Monty Python's The Meaning of Life, and as director, finally gained fuller control of the projects, devising a visual style that allowed the performers 'space'; for instance, in the use of wide shots for long exchanges of dialogue, and more economical use of music.

As demonstrated in many of his sketches with Palin, Jones was also interested in making comedy that was visually impressive, feeling that interesting settings augmented, rather than detracted from, the humour. His methods encouraged many future television comedians to break away from conventional studio-bound shooting styles, as demonstrated into the 21st century by shows such as Green Wing, Little Britain and The League of Gentlemen.

Of Jones's contributions as a performer, his parodic, screechy-voiced depictions of middle-aged women are among the most memorable. His humour, in collaboration with Palin, tends to be conceptual in nature; a typical Palin/Jones sketch draws its humour from the absurdity of the scenario.

For example, in the “Summarise Proust Competition”, Jones plays a cheesy game show host giving a series of contestants 15 seconds to condense Marcel Proust's lengthy work À la recherche du temps perdu; in the "Mouse Organ" sketch, he plays a tuxedoed man using mallets to bash mice who have been trained to squeak at a select pitch, and when “played” in the correct order reproduce the tune "Bells of St. Mary".

In both cases, the laughs originate in the madness of the idea itself. Jones was also notable for his gifts as a Chaplinesque physical comedian, perhaps best demonstrated in the "Undressing in Public" sketch.

He was often cast as the straight man, or as a nerdy or put-upon character, often with ambitions or dreams beyond his abilities, in contrast to the authority figures often played by John Cleese or Graham Chapman.