It was actually cracked by German-speaking Polish mathematicians even before the war broke out (the Enigma had been used for diplomatic communications with German embassies in the 30s). Then once they realized through intelligence gathered with their early version of the bombe that Poland was about to be invaded, they smuggled out all the gear and it eventually wound up in England.

Turing did make significant improvements to the design though, essentially making it programmable, and he is often cited as the father of the modern computer.