Born Edmund Bunney, he was the son of Joseph Bunney and Mary Cradock in Freathby, Leicestershire.
He married in 1777, Anne, the daughter of Joseph Hurlock, Governor of Bencoolen and one of the Directors of the East India Company.
Upon his marriage, Edmund Bunney changed his name to Cradock-Hartopp, as required by the wills of his maternal uncle Joseph Cradock and his wife's maternal grandfather.
[2] In 1792 he acquired Four Oaks Hall, Sutton Coldfield, the town of which he was briefly Warden in 1823.
He died in Bristol in 1833 and was succeeded by his eldest surviving son Edmund.