This is one is actually kind of sad and a good story. It's the Miles M.52.
By 1942, Germany was developing very fast jet and rocket powered aircraft. The British government was looking for an aircraft which could match those speeds. However, due to a mixup between metric and imperial measurements, the specification ended up calling for an aircraft that could reach 1000mph. This would be supersonic flight and was, at the time, widely believed to be impossible. Getting close to the sound barrier was incredibly dangerous, because the massive increase in drag would lock up existing control surfaces and make aircraft unable to maneuver.
So for three years, the Miles aircraft company worked to build a supersonic aircraft noone actually wanted. They solved the theoretical problems of how to maintain control of an aircraft at transsonic speeds. However, the project was cancelled as soon as the war ended, both because of the horrific financial situation after the war and because much of the air force command still believed transsonic flight was impossible. In the end, the M.52 only existed in the form of scale models and design documents and an almost finished prototype. The scale models, incidentally, did achieve controllable supersonic flight.
Under allied technology sharing agreements, the research and specifications for the M.52 were shared with US counterparts, and ultimately many of the innovations were incorporated into the Bell X1. However, after receiving the data the US simply neglected to send anything back (this is actually surprisingly typical of allied technology sharing agreements).
The M.52 was hugely ahead of its time (so ahead of its time that it had to be commissioned by accident). The work which went into designing it made supersonic flight achievable, and yet it never actually flew. It could very easily have been the first manned supersonic aircraft, but instead it's just a sad little footnote in aviation history.