The real u571 was sunk by depth charge and is totally unrelated to the plot of the movie. The movie is loosely based on a combination of the u505 which was in fact captured by the US Navy, and the u110 which was captured by the Brits. The u505 is often left out of the story by the British in keeping with their love of not acknowledging American involvement in the Wars.
u505 was 3 and a half years later in mid 44, and was notable only for gaining current code books. That saved time to crack as by that stage of the war Enigma was being routinely broken. Coming in the week of D Day, of course that proved important.
u110 in 41 provided a breakthrough in that it provided warning of 4 rotor naval Engima long before their introduction. It meant Bletchley had already started preparing for 4 rotor by the time it was introduced. It was the trigger for work on the 4 rotor bombes. There were other U boat captures.
American involvement is impossible to play down - convoys were critical to our survival, and there were tens of thousands of Americans based here for much of the war. I'm often just as disappointed when Hollywood plays fast and loose with mainly US operations like Guadalcanal or Midway. Even so Hollywood movies rarely attract the outcry U571 did at the time of release.
I don't think we love to leave out the American involvement in WW2 at all. There is a huge community of military enthusiasts in the UK and they almost exclusively have American military equipment. My father owns a classic Willies jeep for example.
I just think we prefer to talk about the parts we played, just as any country would.