Powell was born in Tonbridge, Kent, England, the son of a local gunsmith, and educated at a local primary school before gaining a scholarship to the Judd School, Tonbridge, which now has one of its four houses named after Powell (the house colour is green), and awards the Powell Physics and Mathematics Prize to an upper sixth form student every year in his honour. Following this he attended Sidney Sussex College, Cambridge, graduating in 1925 in The Natural sciences. After completing his bachelor's degree he worked at the Cavendish Laboratory, Cambridge, under C.T.R. Wilson and Lord Rutherford, conducting research into condensation phenomena, and gaining his Ph.D. in Physics in 1927.