If I remember my history correctly, the Brits did get their hands on an Enigma machine. They retrieved it from U-Boat 110 and then sank the submarine hoping the Nazis will think the machine went down with the boat to the bottom of the ocean.
Changing the Enigma codes won't really solve the big problem if one of the machines was captured. Once you have the machine, you can figure out how it works and then it's just a matter of time until you're able to figure out the latest code.
Multiple Enigma machines were captured over the course of the war but the key ones that enabled the British to break the codes were captured from the German navy.