Basil James Carker (M.A., Oxon.) was headmaster of Coal Hill School in March 1963. Gillian Roberts called him "Crusty."
Carker announced new school rules in response to the unseasonable cold. When a snowman came to life and injured Francis Minto, Carker sentenced Gillian Roberts and Susan Foreman to detention.
However, after Mr Okehurst and several students were killed by the Cold, Carker's authority broke down. (PROSE: Time and Relative) He was replaced by Harvey Parson. (TV: Remembrance of the Daleks, AUDIO: An Unearthly Woman, PROSE: Nothing at the End of the Lane)