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 child 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. 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.

Fletcher was born in Enfield, North London, and grew up in Woodford Green and Palmers Green; his parents were teachers. He dated his Press Gang co-star Julia Sawalha and also had a relationship with actress Liza Walker. In 1991, he was given a conditional discharge for twelve months and ordered to pay £30 costs after the theft of two bunches of nasturtiums valued at £5 from a stall run by Buster Edwards.

Fletcher presented the third series of Channel 4 show GamesMaster in 1993. Dexter was originally slated to be a special guest on the third series but was then asked to be presenter, after Dominik Diamond left the show due to his disapproval at McDonald’s landing a sponsorship deal with them.

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.

Fletcher recalls presenting GamesMaster was ‘very unforgiving’ and ‘quite intimidating’. He claimed the most difficult part was ‘just getting up, taking a deep breath, and going out there and doing it’. The series finished in 1994 and Dominik Diamond returned for the last four series until the show ended in February 1998. The show’s creator Jane Hewland later said in a retrospective interview, that she sees the third series as a “lost” one, due to admitting to a series of poor decisions and mistakes, including hiring Fletcher as main presenter. His name was however included on a rolling list of acknowledgements, which replaced the usual end credits when the final episode was broadcast, but he has not taken on any other presenting role before or since.

In 1997 he married Lithuanian film and theatre director Dalia Ibelhauptaitė in Westminster. His best man was fellow actor Alan Rickman. Dexter’s brothers are also actors; Graham Fletcher-Cook and Steve Fletcher.

In 1998, Fletcher featured on the song “Here Comes the Flood” from the album Fin de Siecle by The Divine Comedy. In 2014 he narrated the BBC1 show Del Boys and Dealers.

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.

He also appeared in the Boon episode “Walking Off Air”, playing Eddie Cotton. In 2009, he appeared in Misfits as Nathan Young’s dad, reprising the role in 2010 for the second series. Fletcher stars in 2009 in the vampire film Dead Cert, which is directed by Steven Lawson.

2011 saw him acting in his first role as a police officer, as Detective Edwards in the British film noir Jack Falls, alongside his Lock, Stock and Two Smoking Barrels co-stars Jason Flemyng and Alan Ford. In 2012, Fletcher had a small role in horror-comedy Cockneys vs Zombies, where he played the character ‘Dad Maguire’. In 2015 Fletcher played the role of ‘Scooter’ in episode five of the eight-part BBC TV drama The Interceptor. He also took the lead role as history teacher Mr Sheers in supernatural British teen film Coven. In 2016 Fletcher played the role of ‘Paul’ in the cult British crime comedy, Smoking Guns.

Fletcher’s debut as a director was for a script he co-wrote, Wild Bill, was released on 20 March 2012. His second film as director is a musical film by Stephen Greenhorn, Sunshine on Leith based around the popular Proclaimers songs which was released on 4 October 2013. In 2015, he directed the feature film Eddie the Eagle. On 6 December 2017, Fletcher was announced as Bryan Singer’s replacement director on the Queen biopic, Bohemian Rhapsody. The film was released on 2 November 2018. While Fletcher had helped finish the film, Singer received sole directing credit and he received executive producer credit. Fletcher’s latest directing role was on Rocketman, a biopic about the life of Elton John. His next project is going to be Sherlock Holmes 3, the sequel to the 2011 film Sherlock Holmes: A Game of Shadows, expected to release 21 December 2021.