Callow was born in Streatham, London, England, the son of secretary Yvonne Mary (née Guise) and businessman Neil Francis Callow. He attended the London Oratory School and then went on to study at the Queen's University of Belfast before giving up his degree course to go into acting at the Drama Centre in London.

Callow was an established stage actor before making his first film appearance in Amadeus in 1984 (having played Mozart in the original stage production at the Royal National Theatre). His first television role was in Carry On Laughing episode Orgy and Bess, in 1975, but it was cut from the final print.

He starred in several series of the Channel 4 situation comedy, Chance in a Million, as Tom Chance, an eccentric individual to whom coincidences happened regularly. Roles like this and his part in Four Weddings and a Funeral brought him a wider audience than his many critically acclaimed stage appearances.

One of Callow's best-known books is Love Is Where It Falls, a poignant analysis of his eleven-year relationship with Peggy Ramsay (1908-91), a prominent British theatrical agent from the 1960s to the 1980s. He has also written extensively about Charles Dickens, whom he has played in a one-man show, The Mystery of Charles Dickens by Peter Ackroyd,in the film Hans Christian Andersen: My Life as a Fairytale, and on television several times including An Audience with Charles Dickens (BBC 1996) and in "The Unquiet Dead", a 2005 episode of the BBC science-fiction series Doctor Who.

Callow appeared with Saeed Jaffrey in 1994 British television series Little Napoleons. In 1996 Callow directed Cantabile in three musical pieces (Commuting, The waiter's revenge, Ricercare No 4) composed by his friend Stephen Oliver. Ricercare No4 was commissioned by Callow especially for Cantabile.

In 2004, he appeared on a Comic Relief episode of Little Britain. In 2006, he wrote a piece for the BBC1 programme This Week bemoaning the lack of characters in modern politics. He has starred as Count Fosco, the villain of Wilkie Collins's novel The Woman in White, in film (1997) and on stage (2005, in the Andrew Lloyd Webber musical in the West End).

In December 2004, he hosted the London Gay Men's Chorus' Christmas Show, Make the Yuletide Gay at the Barbican Centre in London. He is currently one of the Patrons of the Michael Chekhov Studio London. Callow narrated the audio book of Robert Fagles' 2006 translation of Virgil's The Aeneid.

In July 2006 the World renowned London Oratory School Schola announced Callow as one of their new patrons. In November 2007 he threatened to resign the post over controversy surrounding the Terrence Higgins Trust (an AIDS charity of which Callow is also a patron). Other patrons of the Catholic choir are HRH Princess Michael of Kent and the leading Scottish composer James MacMillan.