He was born in France but moved to England at an early age and was educated at Harrow School and then trained at the Royal Academy of Dramatic Art. His parents divorced when he was very young.
In 1998, Dreyfus won the Best Supporting Performance in a Musical Olivier Award for his work in The Lady In The Dark at the National Theatre. In the same year he was nominated for the Ian Charleson Award for his performance as Cassius in Shakespeare's Julius Caesar at the Birmingham Rep.
Dreyfus' first television break came with the BBC comedy series Absolutely Fabulous. followed by roles as Constable Kevin Goody in Ben Elton's sitcom The Thin Blue Line and Tom Farrell, the gay flatmate of Linda (Kathy Burke) in Gimme Gimme Gimme. Dreyfus played opposite Bette Midler in the short-lived American sitcom Bette.
Known for portraying "camp, endearing characters," Dreyfus (in a Sheengate Publishing interview) compared the character Frank Spencer from Some Mothers Do 'Ave 'Em, who he described as a campy but married heterosexual, to Dreyfus' character Kevin Goody from The Thin Blue Line. Moreover, Dreyfus described Goody as "naïve and silly, and gormless and stupid." In response to viewers' assumptions that the character is gay, Dreyfus said that Goody is attracted to a female character in the series. Regarding his character Tom Farrell from Gimme Gimme Gimme, Dreyfus hypothesized that, even if the character were heterosexual, the actor would still portray Tom as camp and flamboyant. Furthermore, Dreyfus said that he felt that he became typecast due to his portrayals of "flamboyant" characters.
In November 2004, Dreyfus played Carmen Ghia in the London premiere of Mel Brooks' musical The Producers, at the Theatre Royal, Drury Lane. He played the role for 10 months until August 2005.
He played Thermoman in the BBC One comedy My Hero, a role he took over in the sixth series from Ardal O'Hanlon. Although the same character, he used the name George Monday, as opposed to Ardal O'Hanlon's character's name, George Sunday. After disappointing ratings, the show was axed.
Dreyfus also starred as Mr. Teasy-Weasy in the 2004 comedy film Churchill: The Hollywood Years.
In March 2006, he returned to the West End stage in a revival of Michael Frayn's comedy Donkeys' Years at the Comedy Theatre alongside Samantha Bond, David Haig and Mark Addy. He left in August of that year to prepare for his new lead role as the Emcee in a West End revival of Cabaret. In 2008 he appeared in a revival of Simon Gray's The Common Pursuit at the Menier Chocolate Factory.
From September 2009 to January 2010 he appeared in Breakfast At Tiffany's at the Theatre Royal, Haymarket, London.
In January 2012 he appeared in the Midsomer Murders episode "A Rare Bird" as Ralph Ford.
Since 2012 Dreyfus has been appearing as Reverend Roger in the Sky Living series Mount Pleasant.
In February 2015 Dreyfus appeared on stage in Harvey, directed by Lindsay Posner. The production ran at the Birmingham Repertory Theatre until 21 February, before a UK tour and the West End.
In January 2016, he appeared as Dr Herdal in "The Master Builder" at the Old Vic Theatre.
In March 2017 he featured as voice actor on Nevercake's video promoting an event in the video game League of Legends.