Jennings was born in Essex, the son of Peggy Patricia (née Mahoney) and Michael Thomas Jennings. He attended Abbs Cross Technical High School in Hornchurch and then studied English and Theatre studies at the University of Warwick, graduating in 1978. He said he saw his first theatre when he was in high school and went to the Old Vic Theatre, which led him to be inspired to be an actor.
He trained as an actor for two years at the Bristol Old Vic Theatre School.
Jennings began his career in regional repertory theatre, in 1985 playing a range of roles including Maximilien Robespierre in The Scarlet Pimpernel. Jennings met director Nicholas Hytner during this production and has worked with him many times since.
For his performance as Gloumov in Too Clever by Half at the Old Vic, he won the Olivier Award for Best Comedy Performance in 1988. He was nominated in the same category the following year for portraying Dorante in The Liar.
He has performed for the Royal National Theatre in a number of plays, including Leontes in The Winter's Tale and the title role in Albert Speer.
His Royal Shakespeare Company roles include the title role in Peer Gynt (for which he won an Olivier Award 1995-06 for Best Actor), the title role in Richard II (opposite Anton Lesser as Henry Bolingbroke), Theseus/Oberon in A Midsummer Night's Dream (UK, American tour and Broadway), Angelo in Measure for Measure, and the title role in Hamlet. I
In 2002, he appeared in the Cameron Mackintosh/Trevor Nunn revival of My Fair Lady at the Theatre Royal, Drury Lane and won an Olivier Award as Best Actor in a Musical. He was an Associate Artist at the Royal Shakespeare Company.
In 2007, he played the role of Garry Essendine in Noël Coward's Present Laughter at the NT.
In 2011, he played Mikhail Bulgakov in the National Theatre's production of Collaborators.
In 2014, he played the role of Willy Wonka in Charlie and the Chocolate Factory the Musical, which was directed by Sam Mendes and was performed on London's West End theatre district. He took over the role from Douglas Hodge in 2014.
In 2016, he reprised his role as Professor Henry Higgins in the Australian 60th Anniversary production of My Fair Lady, directed by Julie Andrews.
Jennings' work in film includes a portrayal opposite Helen Mirren as Charles, Prince of Wales in the Stephen Frears directed film, The Queen.
He also appeared in War Requiem, the RSC's film version of A Midsummer Night's Dream, Lord Mark in the Oscar-nominated movie The Wings of the Dove, Joseph and the Amazing Technicolor Dreamcoat, and The Four Feathers.
Jennings portrays playwright Alan Bennett in the 2015 film The Lady in the Van opposite Academy Award winner Maggie Smith in the title role. The film is directed by Nicolas Hytner, who is a long-time collaborator from the theatre.
Jennings' work in television includes appearances in The State Within, Smiley's People, The Franchise Affair, Inspector Morse, Lewis, Alfonso Bonzo, the title role in Ashenden, Dead Poets Society, Inspector Alleyn, Hard Times, Bad Blood, and Peter Ackroyd's London. His many radio credits include Casino Royale, The Way of the World, Strange Meeting, Vorbis in Small Gods, and The Old Curiosity Shop. He has also recorded the audio versions of the books The Horse and His Boy, Out of the Silent Planet, and Perelandra by C.S. Lewis, 20,000 Leagues Under the Sea by Jules Verne, and Attention All Shipping by Charlie Connelly, which was selected in June 2008 as one of the top forty audiobooks of all time. He is also a regular narrator on BBC Radio 4's Book at Bedtime.
In 2007, he portrayed the Rev Hutton in the BBC series Cranford. He also played John Le Mesurier in the one-off BBC drama Hancock and Joan.
In 2009, he appeared in The Habit of Art as Benjamin Britten.
In 2010, he played Captain Shipshape in the CBeebies second series of Grandpa In My Pocket and starred in the film Belle. After that, he played Henry Tizard in Castles in the Sky.
From 2011 to 2014, Jennings played Alan Cowdrey QC in the BBC One legal drama Silk. In 2016, he appeared in the Netflix series The Crown as Prince Edward, Duke of Windsor, as well as Leopold I of Belgium in the ITV series Victoria; Leopold was a distant relative of Edward VIII.
In June 2008, he made his operatic debut at the ENO in Robert Carsen's production of Bernstein's Candide, in which he played Voltaire and Doctor Pangloss.
In 2006, he recorded an abridgement of A Spot of Bother by Mark Haddon.
Jennings has won three Olivier Awards:1988: Too Clever by Half - Olivier Award for Best Comedy Performance
1996: Peer Gynt by Henrik Ibsen - Olivier Award for Best Actor
2003: My Fair Lady, playing Henry Higgins, directed by Trevor Nunn - Olivier Award for Best Actor in a Musical
1985: The Scarlet Pimpernel at Her Majesty's Theatre
1987-1988: Measure for Measure by William Shakespeare at Royal Shakespeare Company as Lucio
1988: Too Clever by Half at Old Vic Theatre in London
1988: The Country Wife at Royal Exchange, Manchester
1988: Too Clever by Half at Old Vic Theatre in London
1989: Ghetto at National Theatre as Kittel
1990: The Wild Duck for Peter Hall Company as Hjalmar Ekdal
1990: The Liars at Old Vic Theatre in London as Dorante
1990: Richard II by William Shakespeare at Royal Shakespeare Company as Richard II
1992: The Recruiting Officer at National Theatre as Captain Plume
1993: The Importance of Being Earnest at Aldwych as John Worthing
1994: Peer Gynt by Henrik Ibsen at Royal Shakespeare Company as Peer Gynt
1994-1995: Measure for Measure by William Shakespeare at Royal Shakespeare Company as Angelo
1996: Easter Bonnet Competition at Palace Theatre in New York City
1996: A Midsummer Night's Dream by William Shakespeare in the roles Oberon and Theseus
March 1996 to May 1996: Lunt-Fontanne Theatre on Broadway in New York City
Hyde Park at Royal Shakespeare Company
The Taming of the Shrew by William Shakespeare at Royal Shakespeare Company
1997: Hamlet by William Shakespeare at Royal Shakespeare Company as Hamlet
May 1997 to June 1998: Traveling productions in the United Kingdom and the United States
2000: Albert Speeer at Lyttelton Theatre in London
2001: The Winter's Tale at Royal National Theatre in New York City
2001: The Relapse at Royal National Theatre in New York City
2001: My Fair Lady at Royal National Theatre as Professor Henry Higgins
2003: Brand at Theatre Royal Haymarket in London
2009: The Habit of Art by Alan Bennett for National Theatre of Great Britain as Henry
November 2009 to September 2010: Lyttelton Theatre in London
2011: Collaborators by John Hodge for National Theatre of Great Britain as Mikhail Bulgakov
October 2011 to June 2012: Cottesloe Theatre in London
2012: Hymn by Alan Bennett for National Theatre of Great Britain
November 2012 to March 2013: Lyttelton Theatre in London
2012: Cocktail Sticks by Alan Bennett for National Theatre of Great Britain
December 2012 to March 2013: Lyttelton Theatre in London
2013: Charlie and the Chocolate Factory by Roald Dahl as Willy Wonka
May 2014 to May 2015: Theatre Royal Drury Lane in London
2016: My Fair Lady at Sydney Opera House as Professor Henry Higgins
1999: Joseph and the Amazing Technicolor Dreamcoat as Butler
2010: National Theatre Live: The Habit of Art as Henry / Benjamin Britten
2011: National Theatre Live: Collaborators as Mikhail Bulgakov
2013: National Theatre Live: 50 Years on Stage as Henry Higgins
1989: War Requiem as Blinded Soldier
1996: A Midsummer Night's Dream as Theseus / Oberon
1997: The Wings of the Dove as Lord Mark
2002: The Four Feathers as Colonel Hamilton
2004: Five Children and It as Father
2004: Bridget Jones: The Edge of Reason as Horatio
2006: Babel as Ken Clifford
2006: The Queen as Prince Charles
2008: The Disappeared as Adrian Ballan
2010: Words of the Blitz as George Orwell
2013: Trap for Cinderella as Chance
2013: Belle as Lord Ashford
2014: Castles in the Sky as Henry Tizard
2015: The Lady in the Van as Alan Bennett
1982: Smiley's People (TV Mini-Series) as P.C. Hall (1 episode: "Episode No. 1.1")
1991: Ashenden (TV Mini-Series) as John Ashenden (4 episodes)
1991: Bye Bye Columbus (TV film) as King Ferdinand
1994: Hard Times (TV Mini-Series) as Bitzer (1 episode: "Episode No. 1.1")
1997: Liberty! The American Revolution (TV Mini-Series) as King George III (6 episodes)
1999: The Hunley (TV film) as Lt. Alexander
2001: Bad Blood (TV film) as Joe Harker
2002: Great Britons (TV Mini-Series documentary) as Churchill (voice) (1 episode: "Sir Winston Churchill")
2004: London (TV film) as Stephen Spender
2005: A Very Social Secretary (TV film) as Alastair Campbell
2005: Riot at the Rite (TV film) as Sergei Diaghilev
2008: Fairy Tales (TV Mini-Series) as Roger Bateman (1 episode: "Rapunzel")
2008: Hancock & Joan (TV film) as John Le Mesurier
2008: The 39 Steps (TV film) as Captain Kell
2009: The Last Days of Lehman Brothers (TV film) as Timothy 'Tim' Geithner
2010: On Expenses (TV film) as Andrew Walker
2012: We'll Take Manhattan (TV film) as John Parsons
2013: The Lady Vanishes (TV film) as The Professor
2015: Churchill's Secret (TV film) as Anthony Eden
1986: Kit Curran as PC Woods (1 episode: "A Sick Society"
1988: The Franchise Affair as Nevil Bennet (6 episodes)
1989: The Return of Shelley as Jeremy (1 episode: "The Gospel According to Shelley"
1990: Inspector Morse as Victor Preece (1 episode: "The Sins of the Fathers"
1990: Alfonso Bonzo as Alfonso Bonzo (6 episodes)
1992: Screenplay as Byron (1 episode: "Dread Poets' Society"
1993: Alleyn Mysteries as Sebastian Parish (1 episode: "Death at the Bar")
2000: Too Much Sun as Julian Edgbaston-Bowles (6 episodes)
2005: Agatha Christie's Poirot as Dr Roberts (1 episode: "Cards on the Table"
2006: MI-5 as James Allan (1 episode: "Episode No. 5.4")
2006: The State Within as James Sinclair (6 episodes)
2007: Waking the Dead as James Andrews (2 episodes)
2008: 10 Days to War as Vincent (1 episode: "Failure Is Not an Option")
2009: Agatha Christie's Marple as Inspector Curry (1 episode: "They Do It with Mirrors")
2007-2009: Cranford as Reverend Hutton / The Rev Hutton (7 episodes)
2010: Masterpiece Classic as Captain Kell (1 episode: "The 39 Steps")
2010: Grandpa in My Pocket as Captain Shipshape (1 episode: "Captain Shipshape and a Fish Called Bryan")
2009-2010: Whitechapel as Commander Anderson (5 episodes)
2012: Being Human as Griffin (1 episode: "Eve of the War")
2012: Inspector Lewis as Rev Conor Hawes (1 episode: "The Soul of Genius")
2012: New Tricks as Professor Blake (1 episode: "Body of Evidence")
2011-2014: Silk as Alan Cowdrey, QC (13 episodes)
2015: Foyle's War as Clive Ord-Smith (1 episode: "Trespass")
2016: Victoria as King Leopold
2016: The Crown as Prince Edward, Duke of Windsor