Cannon began making films at the age of 16 in 1984, and started a youth experimental theatre group at 33 Arts Centre. Using the centre's facilities, he was a very prolific director of video dramas and collaborated with a number of other directors in different roles including cameraman. A major influence was the centre's video maker, Dermot Byrne with whom he worked on a number of projects. It was at 33 that he met the future film composer David Arnold who played in a band that rehearsed there. Cannon convinced Arnold that he could compose soundtracks for his and other people's videos. Arnold's first but not the last soundtrack for Byrne was 'The Undead' written by Keith Moyes.
In 1987 Cannon, then a teenager, entered a competition in the British comic 2000 AD to design a poster for a possible future film of Judge Dredd. His work was published in the comic's "Prog 534" edition. In his poster, a clearly Blade Runner–inspired Cannon imagined that the director of the film would be Ridley Scott, with Harrison Ford starring in the title role and Daryl Hannah co-starring as "PSI Anderson".
By 1987 he was awarded the BBC Young Filmmaker of the Year Award for a 40-minute short called Sometimes. He enrolled at the National Film and Television School in 1988, from which he graduated in 1990.
He wrote and directed Strangers (1990) and The Young Americans (1993), the latter having as its title song, "Play Dead", sung by Icelandic diva Björk. Based on his work on the later gangster film, producers signed him to direct the big-budget, but ultimately poorly received film Judge Dredd (1995), starring Sylvester Stallone. Since then he has also directed Phoenix (1998), and I Still Know What You Did Last Summer (1998). Beginning in 2000, he has directed and produced various CSI television series. In 2005 he directed Goal!. Cannon also plays football regularly with Hollywood United F.C. The team mostly features celebrities and former professional footballers. They do however, occasionally play against professional teams for friendly matches and charity events.
He directed a 2006 CBS television pilot, Capital Law, about a group of legal associates trying to make partner at a powerful Washington, D.C.–based law firm. More recently, Cannon co-created TNT's crime drama series starring Dylan McDermott, called Dark Blue. Cannon also directed the pilot episode for Dark Blue.
In 2010, Cannon joined The CW action series Nikita, as director and executive producer.
In 2011, Cannon executive produced and directed the pilot for the FOX crime/mystery Alcatraz.