One of the motivations behind making this movie was the indignation of many British World War 2 veterans (and civilians) over the movie U-571 (2000), in which the capture of the Enigma was shown to be done by American navy officers (despite the fact that the makers of that movie had indicated their movie to be a work of fiction and no accurate portrayal of the events leading to the capture of the Enigma).
Kate Winslet was pregnant with her daughter during the filming of this movie, so the schedule was arranged around that, and at the end of the movie when her character is pregnant, she didn't need a prosthetic.
The Bletchley Park mansion in this film is not *the* actual Bletchley Park mansion, but another property. According to the tour guides at the real thing, the real Bletchley Park did not look enough like Bletchley Park to the production company to have been used in the film.
The railway station used in the film is Loughborough Central on the Great Central Railway, which is about two miles from Garats Hay (Old Woodhouse) which is one of the Y stations mentioned in the film.
Kate Winslet came under criticism from some of the surviving women who served at Bletchley Park during the war because of her dowdy clothes and appearance. The women insisted that even though the country was at war and rationing was the order of the day, they always dressed as best as they could and always maintained a refined appearance. Winslet's only comment about this criticism was that she had no input on how her character looked; that was all down to costume designer Shirley Russell.
In reality, the chief code-breaker was Alan Turing, a homosexual who was prosecuted under the Criminal Law Amendment Act of 1885 (homosexuality was illegal in the UK at the time). While incarcerated, Turing accepted the medical solution of chemical castration. He ultimately committed suicide in 1954. Turing's life is documented in the Oscar-winning film The Imitation Game (2014) where he is played by Benedict Cumberbatch.
Mick Jagger actively pursued the rights for the Robert Harris novel, given his interest in the whole Enigma project. At the same time, former _Saturday Night Live_ producer Lorne Michaels was also after the rights. The two men ultimately decided to pool their resources and co-produce the film.