Williamís parents were William Cook and Catherine Serpell. They were married on 22 December 1819 in Duloe, Cornwall.
They had four children, three of whom survived to adulthood: Mary, Catherine and William.
Whilst Williamís parents are currently unknown, it is thought that Catherine Serpellís parents were Samuel Serpell and Elizabeth Chark. Samuel and Elizabeth were married on 22 June 1784 in Lanreath, Cornwall.