As with
The English Patient, a good movie though far from objective history. It was a Polish team that broke Enigma and created the first "bombe" - they even provided working copies of the enigma machines to England and France in July of 1939; which were largely disregarded. Turing came into play when the Germans added an additional rotor - significant work to be sure but clearly built on the previous work.
"In 1932 a team of young mathematicians from the University of Poznań was set up. Among them were the main code breakers Marian Rejewski, Jerzy Różycki and Henryk Zygalski. It was Rejewski who first cracked the Enigma code, in only ten weeks. His excellent mathematical education, fluent command of German, exceptional intuition and completion of a course in cryptology, together with the intelligence information he received from the French Secret Service, led to his success. The first messages were deciphered as early as Christmas 1932."
https://blogs.bl.uk/european/2018/01/polish-mathematicians-and-cracking-the-enigma.html
There are a lot of other issues, a very good article on some of them here:
Saving Alan Turing from His Friends | Christian Caryl unfortunately most of it is paywalled but the main points:
- Rather than an awkward and robotic genius as portrayed in the movie, Caryle claims that Turing could be charming and had a sense of humor.
- Rather than a “tragic outsider” in “a blinkered society,” Turing was a “willing participant in a collective enterprise.”
- Rather than a small isolated group of codebreakers that achieved no results in the first two years the group “was doing productive work from the very beginning of the war.” In addition, the group was much larger than the small cohort seen in the movie.
- The director Tyldum and screenwriter made up the subplot with the interaction between John Cairncross (the Soviet spy) and Turing.
All that said, it's still an enjoyable movie! It just should not be mistaken for history (as it commonly is).