It’s a fascinating, if troubling, thought to imagine how different the world would be without Professor Alan Turing having been in it.

Recounting a compliment given to him at school by his best friend Christopher, the person who would have the greatest impact on his life, Turing notes that “sometimes it is the people no one imagines anything of who do the things that no one can imagine”.

How true. Not only did Turing break Nazi Germany’s Enigma code, but the machine he created to achieve what had previously been thought impossible also unlocked the building blocks that ushered in the computer age.

His reward for all this? Chemical castration at the hands of a British government that at the time regarded homosexuals like Turing as illegal deviants.

While Morten Tyldum’s fine adaptation of Andrew Hodges’ book Alan Turing: The Enigma dwells more on Turing the code breaker, his homosexuality isn’t swept under the carpet as some critics have unfairly judged. Rather, it chooses to define its central, enigmatic protagonist by the remarkable accomplishments he made first and his sexuality second.

Whether you agree with that approach or not shouldn’t detract from what is a taut and gripping thriller featuring yet another towering performance from Benedict Cumberbatch in the central role of the complex and difficult Turing.

One of the most interesting, and potentially controversial, aspects of The Imitation Game is its unspoken suggestion that Turing was possibly autistic. The difficulty he has in the film interacting with people, including fellow Bletchley Park code breakers Hugh Alexander (Matthew Goode), John Cairncross (Allen Leech) and Peter Hilton (Matthew Beard); his struggle to understand how others feel and think; and the trouble he has expressing his thoughts and feelings about anything except his beloved decryption machine seem to imply this, although we can never know for sure, of course.

The only real connection he makes, aside from school friend Christopher (Jack Bannon), is with Keira Knightley’s Joan Clarke, although even this bond is more intellectual than anything else. While Turing insists that Joan be given the chance to prove herself (to the frustration of some of his more sexist colleagues) his position isn’t dictated by seeking gender equality; rather he sees a person who can contribute towards realising his single-minded obsession to perfect the code-breaking device.

Tyldum does an effective job of wringing the tension out of the key moment when the breakthrough is made and we, as much as Turing and his team, suddenly comprehend the seismic impact of what they’ve achieved. This is then nicely undercut by the terrible realisation of what they must – and must not – do in order to maintain the illusion to the Germans that Enigma remains unbroken.

The awful personal and professional burden of preserving secrets at all costs eats away at Turing, who ostracises himself so much from Joan and the others that the only person he can turn to is pragmatic MI6 operative Maj. Gen. Stewart Menzies (Mark Strong).

A cast studded with British thespian talent eats up the material, in particular Charles Dance as Turing’s brusque commanding officer Cdr. Alastair Denniston and Rory Kinnear as the detective who digs into Turing’s past after the war, only to realise too late what he’s done. Knightley holds her own in the film’s only major female part and imbues Joan with more than just plucky English stoicism; there’s a steeliness to her performance and a refreshing depth the actress hasn’t always plumbed.

Alex Lawther gives a marvellous turn as the young Turing, an “odd duck” who betrays a gamut of emotions in a single glance towards fellow pupil Christopher – his is a name to watch out for in the future. Cumberbatch, meanwhile, does a superb job of showing just enough of the brilliant professor while still remaining an enigma.

The Imitation Game may not quite discover the unwritten code to great cinema, but it remains an engrossing account of a remarkable man’s world-changing accomplishments.