After graduating, Griffiths earned a spot on BBC Radio. He also worked in small theatres, sometimes acting and sometimes managing. He built up an early reputation as a Shakespearean clown with portrayals of the Constable in The Comedy of Errors and Falstaff in The Merry Wives of Windsor with the Royal Shakespeare Company, and went on to play the King in Henry VIII.
He eventually settled in Manchester and began to get lead roles in plays. From there he began to appear on television and then got his big break in film in It Shouldn't Happen to a Vet (1975). By the early 1980s he was selected for the lead role in the BBC drama serial 'Pig In The Middle', an early computer-conspiracy thriller. His character, Henry Jay, was reprised in Bird of Prey (1982). He went on to supporting roles in a number of major films, including The French Lieutenant's Woman, Chariots of Fire, and Gandhi. On stage, in 1985–86 he performed the role of Verdi in Julian Mitchell's After Aida, in Wales and at the Old Vic Theatre in London.
Griffiths' more recognised film roles have been in both contemporary and period pieces such as Gorky Park (1983), Withnail and I (1987), King Ralph (1991), The Naked Gun 2½: The Smell of Fear (1991), Guarding Tess (1994), and Sleepy Hollow (1999). Recently he has been seen as Harry Potter's cruel uncle Vernon Dursley in the Harry Potter series (Harry Potter and the Philosopher's Stone, Harry Potter and the Chamber of Secrets, Harry Potter and the Prisoner of Azkaban, Harry Potter and the Order of the Phoenix, and Harry Potter and the Deathly Hallows – Part 1; the Dursleys were absent in Harry Potter and the Goblet of Fire and Harry Potter and the Half Blood Prince.)
Although typically known for comic performances, he is probably best recognised, aside from Harry Potter, as Inspector Henry Crabbe, disillusioned policeman and pie chef extraordinaire, in the British detective drama Pie in the Sky, a role which was created specifically for him. He also made an extended appearance in the 2005 version of Charles Dickens' Bleak House. In 2004, he originated the role of Hector (the teacher) in Alan Bennett's play The History Boys, directed by Nicholas Hytner, winning the 2005 Laurence Olivier Award for Best Actor. During the play's subsequent United States run, he added a Drama Desk Award, an Outer Critics Circle Award, and a Tony Award. He reprised his role in the film version which was released in October 2006. Together with his Harry Potter co-star Daniel Radcliffe, who plays Harry Potter, he appeared in a stage revival of Peter Shaffer's Equus at the Gielgud Theatre in London, and later from October 2008 in a short run of the play at the Broadhurst Theatre on Broadway which ended in February 2009. Later in 2009 he replaced Michael Gambon as WH Auden prior to the premiere of The Habit of Art at the National Theatre, once again directed by Hytner.
Griffiths was considered for the part of the Doctor in Doctor Who following Tom Baker's departure in 1981, but was unavailable. He was strongly considered once again to take on the role of the Eighth Doctor, had the series continued past 1989.[5] Coincidentally, his two principal co-stars from Withnail and I –Paul McGann and Richard E. Grant– went on to play the role in some capacity.[6] Griffiths has also performed in adaptations of the Hitchhiker's Guide to the Galaxy, providing the voice for Slartibartfast for the radio adaptation of Life, the Universe and Everything and playing the Vogon Jeltz in the film version of The Hitchhiker's Guide to the Galaxy. He has also appeared in Bedtime Stories with Adam Sandler, and as a special guest in A Muppet Christmas: Letters to Santa.
During a performance of The History Boys, Griffiths became so annoyed at a man in the audience whose mobile phone rang repeatedly through the play that Griffiths stopped acting after the sixth time and ordered the man out of the theatre. More recently, Griffiths asked an audience member to leave a performance of Heroes after her phone rang three times.[7] This interruption of a performance due to audience distraction has happened no fewer than three times in his career.[8][9][10]
Griffiths appeared as King George II in 2011's Pirates of the Caribbean: On Stranger Tides.[11]
He appeared in the first episode of Episodes, a show featuring Matt LeBlanc, as Julian Bullard.
In April 2012, Griffiths will star, alongside Hollywood actor Danny DeVito, in a revival of the Neil Simon play The Sunshine Boys. The show will preview at the Savoy Theatre from 27 April 2012, opening on 17 May and playing a limited 12-week season until 28 July.[12]