This is an impressively made movie from 1952 spanning the years between the end of WW2 and the Sputnik era.
In some ways, it is a science fiction movie. It has the right spirit for a classic, "real" sci fi novel or movie, as distinguished from almost all of those produced in the last 25+ years, which are primarily filled with irony, self- deprecating humor, pessimism, decadence, and gratuitous violence. Everyone born since, say, 1965, should see this to get the real spirit of science fiction.
As others have posted, it really is fiction. The fact that Chuck Yeager broke the sound barrier in 1947 was kept top-secret for several years. This movie was in the middle of production when the story broke. According to Robert Osborne on TCM, the director and producer considered including a reference to Yeager, but wisely, I think, decided to continue with the original plot and screen play. It is also fictional in the explanation for how to control the plane as it passes Mach 1, but that is a minor point.
However, it is also based on fact. The problems and fears about exceeding Mach 1 were very real. Some of the basic characters are clearly modeled on Geoffrey de Havilland, father and son. It would be almost, but not quite, a spoiler to read about them before seeing the movie.
The script and acting are excellent. It is very good that they emphasize the tension between the father and daughter. The resolution of that tension is very good indeed.
About the only criticism I can make is the choice of the actress to play Susan, the daughter and wife. She seems too old, and in real life, was only seven years younger than her "father."
I am very glad that I saw this optimistic, yet realistic, look at the motivation and risks of aeronautic and space exploration, coming from the golden age of British cinema.