Much-in-demand actor Benedict Cumberbatch shines as yet another enigmatic character in this film about brilliant English mathematician and code-breaker Alan Turing, the man Winston Churchill described as making the single greatest contribution to the Allied victory in World War II. With a superb supporting performance from Keira Knightley, the film is a captivating thriller despite an absence of any large-scale cinematic action.

The story centres on Turing as he joins an elite group at the British Government's top-secret Code and Cypher School – all trying to crack the infamous Enigma machine that encrypted German military messages. An anti-social oddball, Turing is regarded with disdain by fellow boffins Hugh Alexander (Matthew Goode) and John Caincross (Allen Leech) and is sacked by his commanding officer and boss Commander Denniston (Charles Dance) who finds his haughty attitude infuriating. But Turing appeals to prime minister Winston Churchill, who not only reinstates him, but makes him the team's leader. Suddenly untouchable, Turing recruits new blood – including Joan Clarke (Knightley) and starts building an expensive and monstrous mathematical machine capable of crunching through the permutations of German encryption. As they get closer to cracking the code, everyone begrudgingly comes to respect Turing's annoying brilliance and a romance develops between him and Joan.

Framed by the rather unnecessary story of Turing's arrest for indecency in 1952 by Detective Nock (Rory Kinnear), the film also reveals the young Turing (Alex Lawther) at school in the 1920s when his genius and awkwardness were first recognised, and ends with a distracting polemic about Turing's treatment as a homosexual by British authorities. These plotlines detract from the central drama of Turing's work during the war and ultimately turn the film into a biopic of Turing from childhood to death. But there's no taking away from the performance of Cumberbatch, who plays the complex, dignified, fragile and rather impenetrable man with a sensitivity that will surely bring an Oscar nomination.

Written by Graham Moore, the script was optioned by Warner Brothers only to be rejected after nine months in development because it was thought to be too small a concept – an insight into the film's intimate, rather than epic, nature. Norwegian director Morten Tyldum (Headhunters) keeps the focus on the key relationships and creates a strongly cohesive story world thanks to designer Maria Djurkovic (who also designed Tinker Tailor Soldier Spy, Vanity Fair and Sylvia). AlexandreDesplat's excellent music works best when supporting the film's true drama – how an idiosyncratic smart-arse became the irresistible personality force behind a secret operation that saved millions of lives.