He was born in Grimethorpe, Yorkshire and won an open scholarship to Emmanuel College, Cambridge in 1942. However, he was called up for military service and served in the Royal Air Force during the Second World War. He went to Oxford in October 1947 before moving to Reading University in 1949 to study a diploma in education.^[1]

From 1951 until 1954 he was an assistant lecturer at Reading, after being appointed by Arthur Aspinall, the professor of history. Smith was successively lecturer (1954–64), senior lecturer (1964–76) and reader (1976–90) at Reading.^[1]

Smith was employed by both Aspinall and Lewis Namier as a research assistant on The History of Parliament project. He was also joint editor (with Aspinall) of English Historical Documents, 1783-1832 (1959).^[1]

His first book was a biography of William Fitzwilliam, 4th Earl Fitzwilliam, a Whig politician. His biography also shed light on the survival of Whig principles from the age of Lord Rockingham and Edmund Burke to the era of Charles Grey and Lord John Russell.^[1] Smith wrote a biography of Grey, which was published in 1990, and a biography of George IV, published in 1999. In his last years he was working on a biography of William IV, whom he liked. He also aimed to write the biography George III, whom he considered "an evil old man".^[1]

In 1991 he was awarded a LittD from Cambridge. He was also instrumental in the founding of Reading Festival.^[1]

Smith married Daphine Greenhaigh in 1948, with whom he had a son and a daughter. They divorced in 1978, whereupon Smith married Anne Pallister, who died 1986. In 1988 he married Virginia Willcox. Smith died in Redhill, Surrey on 27 November 1998.^[1]

• Whig Principles and Party Politics: Earl Fitzwilliam and the Whig Party, 1748-1833 (1975)
• Lord Grey, 1764-1845 (1990)
• A Queen on Trial (1993)
• George IV (1999); for the Yale English Monarchs series