Well,
I didn't mean for this to turn into a US vs. UK fight, because it really isn't.
I would make two assertions,
First, that the claim that the U.S. "stole" the technology stems from a post war frustration with the British Govt's cut of a program that was poised to achieve a dramatic leap forward in aviation technology. The actual term for "Sound Barrier" stems from a British journalist's mis-characterization of a problem in physics as described by researchers in the field. This created a vision of some sort of invisible barrier which would destroy all aircraft that approached it. This wasn't true of course, and engineers knew that, but it was built up in the public's imagination. When the desire to "break" that barrier was established, and then walked away from, there was significant frustration in the press. Further, since the U.S. was still developing the technology and became the beneficiary of the joint research, the assertion was made that the U.S. "stole" the technology. That ignores the pre-war research done, primarily by the NACA in the U.S. on the same problem, which was shared with the UK under the terms of the agreement. The Miles project benefited from that research, just as the Bell X1 benefited from the Miles aircraft.
Secondly, with the cancellation of the joint project on the UK side, the US had no one to provide research to. There were certain parts of the US project which was kept close hold, mostly due to patent restrictions but there's no evidence that the US unilaterally walked away from it's agreements with the UK. By now, both the US and the UK had a pretty good understanding of the engineering science involved in building fast aircraft, but were now moving in different directions.
Nonetheless, British pride took a significant hit with he cancellation of the Miles project, and in frustration the allegation has always been that the US researchers somehow stole the secrets of supersonic flight. I've seen nothing to justify that claim. It appears rather that the two nations benefited from their joint research, but in different ways, and that the UK decision not pursue the sound barrier was an internal political decision. I would also point out that in the immediate post war years the UK was attempting to determine it's defense priorities and what would be important for the next generation of aircraft. So, while we as aviation enthusiasts can criticize that decision, we do so with the benefit of hindsight and with no real perspective on the problems of the UK national defense strategy at that time and its priorites. In other words, we don't know what we don't know.
I would add, that most engineers agree the Miles prototype undoubtedly was capable of breaking the sound barrier. The fact remains however, that it did not.