Jack Bonham-Carter was the son of Joanna Maria Smith (1792–1884) and the Portsmouth Member of Parliament John Bonham-Carter (1788–1838). Among his siblings was the artist Hilary Bonham Carter, a friend of political journalist Harriet Martineau, and Elinor Mary Bonham Carter, the wife of prominent jurist Albert Venn Dicey.
His paternal grandparents were Dorothy (née Cuthbert) Carter and Sir John Carter, who served as Mayor of Portsmouth. His maternal grandfather was abolitionist William Smith and through his aunt Frances, he was a first cousin of Florence Nightingale. His maternal uncle was Whig politician Benjamin Smith, father of his first cousins Barbara Bodichon and Benjamin Leigh Smith.