Henry Yates Thompson was born near Liverpool, England, in 1838, the eldest son of prosperous banker Samuel Thompson, and his wife, Elizabeth Yates. He was an 1862 graduate of Trinity College, Cambridge, where he studied classics and won a prize for his knowledge of Greek. Although he was trained as a barrister at Lincoln's Inn, he never practiced law. For six months in 1863, he traveled around the United States, where he witnessed Ulysses S. Grant leading forces at the Battle of Chattanooga and developed great sympathies for Union and abolition causes. Upon his return to England, he was struck by the ignorance of American culture among the British upper class, and in 1865, proposed a lectureship on American history at Cambridge to be held by a lecturer chosen by Harvard College. Although Thompson received the support of Thomas Hill, President of Harvard, Cambridge ultimately rejected the idea. From 1868-1873, he was private secretary to John Spencer, 5th Earl Spencer, Viceroy of Ireland.
In 1878, he married Elizabeth ("Dolly") Smith, daughter of publisher George Smith. Thompson owned the Pall Mall Gazette, a gift from his father-in-law, from 1880-1892. After its sale, he devoted himself to the collection of illuminated manuscripts and became a benefactor of the British Library. He died in 1929.