Professor Frayling correctly stated that Chuck Yeager had already broken the sound barrier in 1947, before the events in the British film supposedly took place. Rattigan knew this, but his reference to it in the script was cut out. He may also have known the history of the real British research carried out by the Miles Aircraft Company in the 1940s, research which was shared with the American Bell company under a wartime agreement. Both Yeager's exploit, and the research by Bell and Miles, remained official secrets for many years. Wikipedia says:
Frayling was plain wrong when he said that audiences didn't know what jets were in 1952. Both the Gloster Meteor and the de Havilland Vampire were in service in increasing numbers with the RAF and a familiar sight (and sound) near air bases in the late 1940s. The Comet (which features in The Sound Barrier) made its debut in 1952 but had already gained much press attention.