The story is deeper than the Enigma project. Flashbacks to Turing's boyhood illuminate his homosexuality. Perhaps deeper is a conversation with his close friend, Christopher (near as I can recall):

Christopher is reading a book about codes and ciphers.
Alan: Secret messages?
Christopher: Not secret. Anyone can read them, but no one knows the meaning.
Alan: How is that different from talking? People say things they don't mean all the time. And when they talk to each other, everyone seems to know what they are talking about, but I never do.

Later, being introduced to Bletchley Park, it comes out twice or thrice that Alan does not "get" jokes. Past the halfway point, Joan explains that he needs the cooperation of other people on the team he now heads in order to be successful at this project. He must get them to like him. He bridges the gulf with the team by giving them each an apple and then telling a well-worn joke. (Two men are in the woods and come upon a bear…. No, I only need to run faster than you.) He is smart enough and dispassionate enough to address his difficulties in socialization.

Unfortunately, when he is arrested for "gross indecency" (homosexuality), he does not attempt to deny it. In the biographies I read, he was frank with his interrogators, never seeming aware of the consequences of his confession. It apparently never sunk in that his behavior even should have been illegal. Now, we share his viewpoint; but he was not cognizant of his social context. In the movie, another team member (a Soviet agent, in fact, himself perhaps gay), warns him explicitly that his behavior is against the law and could cost him his place at Bletchley Park. The point to be underscored is that Turing needed to be told that.