Grant was a member of the Space Theatre Company in Cape Town before moving to London in 1982. He later stated, “I grew up in Swaziland when it was mired in a 1960s sensibility. The kind of English spoken where I grew up was a period English sound and when I came to England people said, ‘how strange’. Charles Sturridge, who directed Brideshead Revisited for TV, said, ‘you speak English like someone from the 1950s’.”

Grant married voice coach Joan Washington in 1986 and has one daughter with her, Olivia, and a stepson, Tom. Grant is a teetotaller. His body has an intolerance of alcohol, having no enzymes in the blood to metabolise it. If he does drink alcohol, he can keep it down for 10 minutes and is then violently sick for 24 hours afterward. After casting him as the alcoholic Withnail, director Bruce Robinson made Grant drink a bottle of champagne and half a bottle of vodka during the course of a night so that he had experienced the sensation of being drunk. He is a fan of Barbra Streisand and has done a tour of Streisand’s New York, visiting her early home, her high school, and the Village Vanguard, among other places.

In 1995, Grant starred as the titular character in Peter Capaldi’s short film Franz Kafka’s It’s a Wonderful Life. The film won the 1995 Academy Award for Best Live Action Short Film. In 1996, he portrayed a hilarious Sir Andrew Aguecheek in Trevor Nunn’s film of Twelfth Night. He released a single and accompanying video “To Be Or Not To Be” with Orpheus in 1997.

In 2003 Grant costarred in Posh Nosh, a spoof of cooking shows on BBC.

On 1 December 2006, Grant turned real-life investigator when, with the help of the BBC’s Newsnight, he exposed a $98 million scam to sell a bogus AIDS cure.

Grant appeared as “The Voice” in 2+2+2 at American Nights at The King’s Head Theatre, from 3 to 29 July 2007, and in 2008 co-starred in the London-based comedy Filth and Wisdom. On 22 November 2007, he gave a keynote speech at North London Collegiate School in north London as part of their Performing Arts Centre Opening Festival, and presented the 2008 Laurence Olivier Awards.

In 2008, he made his musical theatre debut with Opera Australia, playing the role of Henry Higgins in My Fair Lady, at the Theatre Royal, Sydney, a role he reprised in 2017 at the Lyric Opera of Chicago. In 2009, he played Alain Reille in Yasmina Reza’s one-act play God of Carnage at the Theatre Royal, Bath: and subsequently at Cheltenham, Canterbury, Richmond, Brighton and Milton Keynes.

In October 2008, Grant told The Times that he is an atheist. He is an avid supporter of Premier League football club West Ham United. In April 2014, Grant launched his new unisex perfume, JACK, exclusively at Liberty of Regent Street, London. Grant runs the perfume business in collaboration with his daughter.

In 2010 he made an appearance in a music video, when short lived Bristol band The Chemists hired him to appear in their video for “This City”; the band split the same year. This appearance also followed up his previous involvement with the band the year before, in which he spoke the lyrics to “This City” to background music, as part of the intro and outro tracks on their only album Theories of Dr Lovelock.

Grant made his first official Doctor Who appearance in the 2012 Christmas special, titled “The Snowmen”, in which he plays the villain, Walter Simeon. During the episode Simeon is erased from his body and it is taken over by the Great Intelligence, voiced in that episode by Ian McKellen until the takeover. The Great Intelligence is one of the Second Doctor’s most infamous villains and, was last seen in The Abominable Snowmen and The Web of Fear. Grant reprises the role in “The Bells of Saint John” and in the series 7 finale, “The Name of the Doctor”.

Grant was a mentor on the British Airways Great Britons Programme. In March 2013 Grant starred as intelligence analyst Brian Jones in David Morley’s drama The Iraq Dossier, with Peter Firth, Anton Lesser, David Caves, and Lindsay Duncan. It recounted the story of how British Ministry of Defence Intelligence expert Jones had tried to warn that his government’s September Dossier on Iraq’s Weapons of Mass Destruction was inaccurate. In 2014, Grant was cast on the HBO series Girls because Lena Dunham saw him in Spice World.

On 9 May 2015 Grant gave a reading at VE Day 70: A Party to Remember in Horse Guards Parade, London. In 2016 Grant joined the HBO series Game of Thrones in Season 6 as Izembaro.

In 2017, he starred as Zander Rice, the main antagonist of Logan, opposite Hugh Jackman, in which he gained positive critical reception for his performance.

In July 2018, Lucasfilm announced that Grant would appear in Star Wars: The Rise of Skywalker. That same year, Grant’s critically lauded performance as Jack Hock in Can You Ever Forgive Me? (2018), earned him Academy Award, BAFTA, Golden Globe and Screen Actors Guild Award nominations. The part also won Grant a New York Film Critics Circle Award and several other critics awards. In March 2020, Grant joined the cast of Loki series on Disney+, though his role is yet to be revealed.