Cohen was born 19 September 1933 in Norwich, but grew up in Stoke Newington. His father was killed shortly after the end of the Second World War, 1 September 1945. His grandfather was a rabbi and Cohen was an observant Jew in his youth. He continued to attend the synagogue for cultural reasons. He was married three times, and had six children. He was a British reproductive biologist also known for his science books and involvement with science fiction.