Fletcher trained at the Anna Scher Theatre drama club. Fletcher's first film part was as Baby Face in Bugsy Malone (1976). He made his stage début the following year in a production of A Midsummer Night's Dream. As a child actor, Fletcher was a regular feature in British productions in the early 1980s such as The Long Good Friday, The Elephant Man, and The Bounty. As an adult, he has appeared on television as rebellious teenager Spike Thomson in Press Gang and also Murder Most Horrid (1991) with Dawn French. His American accent had some fans convinced that he actually is an American. He has starred in the films Caravaggio (1986), The Rachel Papers (1989), Lock, Stock and Two Smoking Barrels (1998), Layer Cake (2004), AffirmFilm's Solomon as Rehoboam, and Universal's Doom as a communications officer nicknamed "Pinky".