Biddle was a talented swimmer in his youth. It was through this that he broke into the film industry. In 1969 the underwater photographer Gil Woxholt hired him to be his apprentice. In this capacity he worked, uncredited, on both the James Bond film On Her Majesty's Secret Service (1969) and Murphy's War (1971). After this, Biddle worked for Ridley Scott's advertising company RSA. He worked on a large number of adverts with Scott and when Scott moved into films, Biddle followed him. On The Duellists (1977) he worked as a clapper loader, before advancing to the position of focus puller on Alien (1979).

Following Alien, Biddle returned to working as a cinematographer on adverts. During this time he developed a number of new lighting techniques and worked on a number of famous campaigns. His most famous advert was 1984 (1984), directed by Ridley Scott, for Apple. The advert's photography, combined with a personal recommendation from Scott, prompted James Cameron to hire Biddle as his cinematographer for Aliens (1986), this was the first film Biddle worked on in this role.

Biddle went on to work as a cinematographer on a further twenty-five feature films, including Thelma and Louise (1991), for which he received a nomination for the Oscar for Best Cinematography. In 1997 he was voted as the European Cinematographer of the Year for his work on The Butcher Boy. The last film that he worked on, prior to his death from a myocardial infarction, was V for Vendetta (2006) which was dedicated to his memory.

His brother is cinematographer Adam Biddle.