Sessions attended RADA in the late 1970s, studying alongside Kenneth Branagh; the two would work together on many occasions later in their careers. In the early 1980s he worked on the small venue comedy circuit with largely improvised freewheeling fantasy monologues. He topped a double bill with French and Saunders during this period. He had a number of small parts in films including The Sender in 1982, The Bounty in 1984 and Castaway in 1986.

Sessions played to his strengths in improvisation and comedy with his one-man stage show Napoleon, which ran in London's West End for some time in the mid-1980s. Sessions and Stephen Fry were the only two regular panellists on the original radio broadcast of Whose Line Is It Anyway? in the late 1980s. When the show, still hosted by Clive Anderson, made the transition to television, Fry departed from regular appearances, but Sessions remained the featured panellist for the first season, a frequent player in the second, but he did not appear again after his two appearances in the third series.

A gifted impressionist (he also voiced characters for Spitting Image), he drew heavily on his extensive literary education and developed a reputation for being "a bit of a swot", being able to quote extensive passages of text and make endless cultural and historical references. His ready ability to switch between accents and personae meanwhile allowed his career in improvisation to flourish. In 1987 he played Lionel Zipser in Channel 4's mini-series Porterhouse Blue.

In 1989, Sessions starred in his own one-man TV show, John Sessions. Filmed at the Donmar Warehouse in London, the show involved Sessions performing before a live audience who were invited to nominate a person, a location and two objects from a selection, around which Sessions would improvise a surreal performance for the next half-hour. This series prompted two further one-man TV shows: John Sessions' Tall Tales (1991) and John Sessions' Likely Stories (1994). Although billed as 'improvisation, these were increasingly pre-planned. In an interview headlined 'Who The Hell Does John Sessions Think He Is?' in Q magazine in the early 1990s, he admitted that some of his improv wasn't entirely spontaneous, but that if it were advertised as scripted 'it had to be funnier'. 1991 also saw Sessions in the BBC drama Jute City, a three-part thriller based around a sinister Masonic bunch of villains, co-starring with vocalist Fish (Derek W. Dick, singer in the first incarnation of rock band Marillion).

This period in his life was unhappy. In a 'Worst of Times' column for The Independent from around 1990, he talked of how the freezing Canadian weather had depressed him, he was smoking 'far too many cigarettes', 'had a couple of disastrous flings' and described his PhD dissertation as '200 pages of rubbish'.

Sessions later returned to formal acting, with parts ranging from James Boswell (to Robbie Coltrane's Samuel Johnson) in the UK TV comedy drama Boswell and Johnson's Tour of the Western Isles (1993) to Doctor Prunesquallor in the BBC adaptation of Gormenghast (2000) and in 1998 as Hercules Fortesque, a BBC HR manager in the BBC mini-series In The Red adapted from the book and the BBC radio series by Mark Taverner. He provided the voice of the Professor in The Adventures of Pinocchio in 1996. He also appeared in several Shakespeare films, playing Macmorris in Kenneth Branagh's Henry V (1989), Philostrate in the 1999 film of A Midsummer Night's Dream, and Salerio in the 2004 movie The Merchant of Venice, with Al Pacino and Jeremy Irons. He also contributed "Sonnet 62" to the 2002 compilation album When Love Speaks (EMI Classics), which consists of famous actors and Musicians interpreting Shakespearean sonnets and play excerpts.

In 1996 he was commissioned by the Royal Academy of Arts to write "Paint, said Fred", the life of Frederic, Lord Leighton, the pre-eminent Victorian Artist, in a one-man show that used his comic writing abilities and his gift for impersonation.

On radio, Sessions guested in December 1997 on the regular BBC Radio 3 show Private Passions, presented by Michael Berkeley, not as himself but as a 112-year-old Viennese percussionist called Manfred Sturmer, who told anecdotes (about Brahms, Clara Schumann, Richard Strauss, Arnold Schoenberg and others) so realistically that some listeners did not realise that the whole thing was a hoax. Other Sessions creations appeared on Berkeley's show in subsequent years. Sessions has taken the role of narrating the popular Asterix stories for audiobook, since the death of Willie Rushton.

In 2006, Sessions presented some of the BBC's coverage of The Proms and featured in one of the two Jackanory specials, voicing the characters and playing the storyteller in the audiobook version of Paul Stewart and Chris Riddell's children's book Muddle Earth. In 2007 he appeared in the final episode of the second series of Hotel Babylon, playing hotel owner Donovan Credo, and as Geoffrey Howe in 2009's Margaret. In 2010 he played Kenny Prince in Sherlock.

Sessions made a guest appearance in a special webcast version of Doctor Who, in a story called Death Comes to Time, in which he played General Tannis. He occasionally appeared in the BBC series Judge John Deed as barrister Brian Cantwell QC. In 2007, he guest-starred in the Doctor Who audio adventure 100.

Sessions appeared in the teen drama TV show Skins in 2011 as one of two adopted fathers of Franky Fitzgerald. He also appeared as a Brummy vicar in an episode of Outnumbered on BBC1.

Sessions has also played two British prime ministers in films, Harold Wilson in Made in Dagenham and Edward Heath in The Iron Lady. In 2013 he appeared in the premiere production of the new play Longing.

In August 2014, Sessions was one of 200 public figures who were signatories to a letter to The Guardian expressing their hope that Scotland would vote to remain part of the United Kingdom in September's referendum on that issue.

He also played the role of Arthur Lowe in the 2015 drama We're Doomed! The Dad's Army Story.

He played Dr Hermann in the 2016 film Florence Foster Jenkins.