Norden was born into a Jewish family in Mare Street, Hackney, in London's East End, and was educated at Craven Park Elementary School and the City of London School where he was a contemporary of Kingsley Amis. Upon leaving school, he worked as a stagehand, moved into cinema management by the age of 17 and quickly progressed to be the manager of a cinema in Watford. He also organised variety shows. He joined the Royal Air Force during the Second World War and was a wireless operator with a signals unit. His writing career began in the Royal Air Force when he wrote for troop shows. Whilst preparing for one of these shows in 1945, Norden, accompanied by fellow performers Eric Sykes and Ron Rich, went to a nearby prison camp in search of stage lighting; the camp turned out to be the Bergen-Belsen concentration camp, which had recently been liberated by the Allies. Norden, Sykes and Rich organised a food collection amongst their comrades to feed the starving camp inmates.