I'm not showing off, and I don't mean to say my opinion is correct, but let's just say I have at least some claim to know what was going on.
I watched the Imitation Game with my wife who knew little to nothing about Bletchley park and Turing. I have to say, that given 90 minutes I couldn't have done a better job in giving them a good feel for the situation and the pressures, the ideas and personalities involved.
I can say with confidence that pretty much everything said or shown in every scene is significantly inaccurate, but taken as a whole, and with an understanding of the restrictions, it's a very good job.
If you can't live without knowing the specific truth, read Hodges. If you can, just watch the film then get on with something else.