Fennessy was born in West Ham, London, on 17 January 1912 and educated at St Bonaventure's Grammar School in Forest Gate. His early academic career was not spectacular, and he graduated with a second-class degree from East London College in 1934. Fennessy had been active experimenting with electrical equipment starting at the age of 10, and this proved useful during the job hunt. He and his fellow East London student Geoffrey Roberts joined Standard Telephones and Cables soon after graduation. Here he worked on "sound location amplifiers".