Williams was born in Tonypandy, Wales, the son of a coal miner. In 1944, he won a scholarship to study at the University of Bristol, where he earned a bachelors degree in 1948 and later a Master of Science in physics. In working to earn his masters degree, he studied stereo micro-radiography at the University of Chicago, under the direction of Cyril Stanley Smith. Around the same time, he also took up a position as a metallurgist with the Revere Copper Company in Rome, New York.
In 1960, Williams earned his doctorate from the University of Toronto.