Gunn was born in Gravesend, Kent, England, the son of Bert Gunn. Both of his parents were journalists. They divorced when he was 10 years old. When he was a teenager his mother killed herself. It was she who had sparked in him a love of reading, including an interest in the work of Christopher Marlowe, John Keats, John Milton, and Alfred, Lord Tennyson, along with several prose writers. In his youth, he attended University College School in Hampstead, London, then spent two years doing national service and six months in Paris. Later, he studied English literature at Trinity College, Cambridge, graduating in 1953 having achieved a first in Part I of the Tripos and a second in Part II. "Fighting Terms", his first collection of verse, was published in the following year. Among several critics who praised the work, John Press wrote: "This is one of the few volumes of postwar verse that all serious readers of poetry need to possess and to study."