He was appointed a professor emeritus of the University of London in 1997.
Williams earned his bachelor's degree and PhD at the University of London.
He became reader in history at Queen Mary College, London and was then promoted to professor.
He served as general editor of the Hudson's Bay Record Society and he has been president and trustee of the Hakluyt Society.
He was survived by his wife and fellow maritime historian, Sarah R. Palmer, and their two children.