The poles claimed to have deciphered the enigma machine as did the british (Mathematician Alan Turing / Bletchley park) and it was the latter centre that was regularly used to decode intercepted messages.
I don't think anywhere in the links you've provided a claim is made that the British were first to break the code. The centre you mentioned used a "technology" which had been first researched by the Poles ten years before.
Honestly I don't think what you said does justice to the history of deciphering the Enigma machine. ("It depends on who you ask, so we don't know.."), but I realize no single statement can do justice to the problem.
If it matters anything, historically it was the Poles who started work on deciphering Enigma, developed the first efficient methodology and achieved considerable success. They shared those secrets with the British, who continued their work for two reasons.
First: Poland considered France and Britain allies (not sure if it was a mutual feeling ).
The Poles, realizing time was running out before the Germans invaded, and unable to extend their techniques with available resources, decided in mid-1939 to share their work, and passed to the French and the British some of their ersatz 'Enigmas', information on Rejewski's breakthrough, and on the other techniques they had developed. The information was shipped to France in diplomatic baggage; the British share went on to Bletchley Park.
I think all of resources you've given are very fair about the subject. I just felt your conclusion wasn't representative of what you can find there. So if anyone's interested, let them read it and draw their wn conclusions.