There are two authors whose name is given as "Earl of Birkenhead" on book covers and title pages.
1. Frederick Edwin Smith, 1st Earl of Birkenhead (1872-1930) Lawyer, politician and close ally of Winston Churchill. His books are listed under Frederick Edwin Smith.
2. Frederick Winston Furneaux Smith, 2nd Earl of Birkenhead (1907-1975) Historian, who wrote, among others, biographies of Rudyard Kipling, Lord Halifax, and his father. His works are listed under Frederick Winston Smith.
They are the same two authors also known as "Lord Birkenhead"