Unsworth was born on 10 August 1930 in Wingate, a mining village in County Durham, England, to a family of miners. His father first entered the mines at age 12 and ordinarily Unsworth would have followed him as a miner. However, when his father was 19, he travelled to the United States for a few years and on returning to Britain entered the insurance business and thus began moving his family up the economic ladder and out of the mines. "He rescued my brother and me from that long chain of continuity that happens in mining villages," Unsworth said.