He married, 21 March 1857, Josephine Elizabeth, only child of Joseph Anstice of Madeley Wood, Shropshire, professor at King's College London.
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Clifford was born in Roehampton, London, the sixth of the eight children of Major-General Sir Henry Hugh Clifford and his wife Josephine Elizabeth, née Anstice; his grandfather was Hugh Clifford, 7th Baron Clifford of Chudleigh.