Wells studied at The Queens College, University of Oxford and obtained his BA and MA in 1934 and 1937, respectively. He then moved to University of Cambridge, where he obtained his PhD in X-ray crystallography in 1939, under the supervision of J. D. Bernal. His PhD thesis was titled The Crystal Structures of Certain Complex Metallic Compounds'. He worked as research scientist at Cambridge from 1937 to 1940 and at University of Birmingham from 1940 till 1944. He moved to the industry afterwards, working as a senior research associate at Imperial Chemical Industries from 1944 to 1968. Wells was not interested in senior administrative jobs offer to him in the industry, he moved back to academia and became a professor of chemistry at University of Connecticut in the US from 1968 until his retirement in 1980.