Hart, the grandson of Irish immigrants, was born one of three children in Liverpool and grew up in a Catholic family. He attended high school in Liverpool and was a member of a theater group as a teenager for young people. Later, he studied drama at college in Liverpool.
As an actor, he was for the first time in the 1990s and actively played in the film Backbeat, which describes the beginnings of the Beatles, the lead role of John Lennon. In 1995, he starred in the movie Land and Freedom also the main role. Finally he was known for his role as Professor Quirrell in Harry Potter and the Sorcerer's Stone.
As a television actor, he embodied in the Dirt series one of the leading roles. He also played the role of Dr. Watson in two Sherlock Holmes television films. For BBC Radio 4 he took over in 2009 in a five-part series on the Tom Ripley novels by Patricia Highsmith, the voice of the title character. In 2011 he played the role of Adolf Hitler in the BBC production The Man Who Put Hitler In The Dock.
Hart is married to the teacher Lynn Hart, with whom he daughter (* 2001). Another daughter (* 1996) comes from a previous relationship.
In 1995, Hart at the International Film Festival in Venice the Volpi Cup for Best Supporting Actor in Boundless Hatred ( Nothing Personal ).