After receiving and elementary education, he was apprenticed at the age of fourteen to Thomas Street, a mathematical and optical instrument maker in Lambeth.
In 1841 he inherited a sum of money, and with his apprenticeship over, he passed two years at the University of Edinburgh, and a period on a walking tour through Europe, paying his way by working as an artisan.
Later he turned his attention to the chemistry and manufacture of paraffin, and was appointed manager of the Leeswood Oil Company in 1863, when he left Birmingham for Caergwrle, Flintshire.
After the decline of the Welsh oil-distilling industry following the discovery of oil fields in the USA, Williams went in 1868 to Sheffield as chemist to the Atlas Iron Works of Sir John Brown & Co.
He delivered the Cantor lectures in 1876, taking for his subject ‘Iron and Steel Manufacture,’ and again in 1878, when he spoke on ‘Mathematical Instruments.’ On the death of his stepfather's brother, Zachariah Watkins, early in 1889, he came into money, and began at the age of sixty-nine what he described as his life-work, the Vindication of Phrenology.
He was author of: He edited Mrs. R. B. Taylor's A B C of Chemistry in 1873, and wrote articles on "Iron and Steel", "Explosive Compounds", and "Oils and Candles" for G. Phillips Bevan's British Manufacturing Industries series in 1876.