He attended a local elementary school and won a scholarship, at the age of eleven, to Judd School, Tonbridge. From there he won open scholarships to Sidney Sussex College, Cambridge, where he graduated with First Class Honours in the Natural Science Tripos (1924-1925).
As a postgraduate student, Powell worked in the Cavendish Laboratory under C.T.R. Wilson and Lord Rutherford until 1927 when he gained his Ph.D. and moved to the University of Bristol as Research Assistant to A.M. Tyndall in the H.H. Wills Physical Laboratory. He was eventually appointed lecturer, then reader and, in 1936, he visited the West Indies as seismologist of an expedition investigating volcanic activity. He returned to Bristol in the following year and in 1948 he was established as Melville Wills Professor of Physics.