Fletcher trained at the Anna Scher Theatre. His 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 youth actor he was regularly featured in British productions in the early 1980s, including The Long Good Friday, The Elephant Man and The Bounty. In 1987 Fletcher was cast in Lionheart. In 1988, he won the Stars de Demain prize at the inaugaral Geneva Cineme Fête for The Raggedy Rawney. As an adult he appeared on television as the rebellious teenager Spike Thomson in Press Gang and in Murder Most Horrid (1991) with Dawn French. He has also 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.
He appeared as Puck in Britten's A Midsummer Night's Dream in 1981 at Glyndebourne Opera and on their autumn tour, and then again in 1990 in an Opera London production at Sadler's Wells, subsequently recorded by Virgin Classics.
On television Fletcher has appeared in the major HBO drama, Band of Brothers and in a supporting role in the BBC One historical drama The Virgin Queen (US PBS 2005, UK 2006). He also appeared in Kylie Minogue's music video for "Some Kind of Bliss" (1997). He starred on BBC One in a series based on Imogen Edwards-Jones's book Hotel Babylon that ran for four series before being cancelled in 2009. He also appeared in "The Booby and the Beast", an episode in the second series of the BBC's series Robin Hood and in the 2008 radio series The Way We Live Right Now. He appeared in the Bo' Selecta! spinoff A Bear's Tail as The Scriptwriter. He played a brief role in the BBC series New Tricks, in the episode "Final Curtain", as an actor named Tommy Jackson. In 2009, he also appeared in Misfits as Nathan Young's dad, reprising the role in 2010 for the second series.
Fletcher has been the voice for McDonald's television adverts and (feigning a US accent) is the narrator of The Game audio book written by Neil Strauss. He also narrated the Five series Airforce Afghanistan, as well as the Chop Shop: London Garage series on the Discovery Channel. In 1993, he was the voice of Prince Cinders in the short animated comedy of the same name. Also in 1993, he was the uncredited UNIT soldier narrator of the UNIT Recruiting Film – a five-minute spoof piece that preceded a BBC1 repeat of the sixth and final episode of Doctor Who story Planet of the Daleks. In 2014 he narrated the BBC1 show Del Boys and Dealers. In 1998, Fletcher featured on the song "Here Comes the Flood" from the album Fin de Siecle by The Divine Comedy.
