The four first-class and four 97p stamps feature portraits of leaders ranging from William Pitt the Younger (1783-1801) to Margaret Thatcher (1979-1990).
Others featured on the stamps are Charles Grey (1830-1834), Robert Peel (1841-1846), William Ewart Gladstone (1868-1874), Clement Attlee (1945-1951), Winston Churchill (1951-1955) and Harold Wilson (1974-1976).
Royal Mail spokesman Andrew Hammond said: "As the United Kingdom is the one of the oldest parliamentary democracies in the world, it is fitting that we mark eight individuals who have held the role over the centuries."
Paul Lay, editor of History Today magazine, said: "This is an intriguing selection of prime ministers, reaching back to the 18th century.
"Some - Winston Churchill, William Gladstone - need little introduction, yet figures such as Charles Grey, the second Earl Grey, though not widely known today, played crucial roles in some of British history's most important events, including the Great Reform Act of 1832, which set the country on the path to mass democracy, and the abolition of slavery."