The Reverend was the son of James Drake-Brockman, High Sheriff of Kent, and his wife, Catherine (Tatton). His grandfather was The Rev. William Tatton, Doctor of Divinity, Rector of Rotherfield, Sussex, and Prebendary of Canterbury Cathedral. William died unmarried and was probably succeeded in the Beechborough estate by his brother, the Rev. Tatton Drake-Brockman.