Rejewski was first to break into any kind of Enigma code, and his work was ground-breaking and often tragically overlooked. But, as best I understand it, the Enigma Code had changed by the time WWII rolled around, and required "re-breaking" -- also, Turing's team broke into other codes like the Lorenz Cipher that Rejewski had never touched.
Also, while the Polish mathematicians handed over a lot of their work -- and, incidentally, were then insultingly given the task of breaking basically the simplest codes in existence, a complete disgrace -- but the Bletchley team ended up using different methods, that were undoubtedly helped by the Polish effort but extended and improved upon them. It's likely, though, that even without the leg-up, Bletchley would still have broken into Enigma at some point, probably a year or two later.
In that sense it's not unlike the question of who invented the lightbulb. A lot of people did, sometimes independently, other times building on previous work, and it can be difficult to say who was first to invent what we mean by a lightbulb. Swan, Edison, Humphry Davy are just three names in the mix.