There was Operation Epsilon, which while the information was sent on to the Americans involved detaining the scientists at Farm Hall, Godmanchester, England. According to this site: "Transcripts of translations of secretly recorded conversations of ten German scientists detained by the British Government at Farm Hall, Godmanchester, England from May 1 through December 1945. The detainment was known as "Operation Epsilon," and the transcripts were sent as reports by the British military officers in charge to their superiors. These reports were then forwarded to the U.S. War Department through the military attache at the British Embassy." So while the German Scientists were detained by the British the work was done on behalf of the Americans.

While I understand this isn't exactly what you were looking for I couldn't find anything else on other Operations. It would appear then that it was the Americans most conducting the operations, but in the case of Operation Epsilon it was the British actually doing the detaining and listening, which was sent to British Officers then to the Americans.

The British and the Soviet Union had their own similar programs. For a raw list of a number of them, Wikipedia's "Similar operations" section on Operation Paperclip is useful.