Harrington was born in Chichester, the son of Emanuel Thomas Poë and Isabella Jane (née Crowdy), and christened Charles Harington. Of Anglo-Irish heritage, Harington gained his unusual name repetition as a four-year-old infant, when his father replaced the family's original surname of "Poë" with the maiden name of Charles's grandmother. His nickname of "Tim", by which he was almost universally known, was acquired while on his inaugural deployment abroad. Fellow officers from his battalion assigned Harington this nickname while en route to Aden after learning of the conviction of Timothy Charles Harrington, an Irish nationalist and Member of Parliament.