Wragge's wife Leonora gave birth to a daughter, Leonora Ingleby, (later renamed Emma) in Oakamoor 1878 and Clement Lionel Egerton in 1880. His third child Rupert Lindley was born in August 1882 in Scotland. Wragge left for Australia soon after in 1883. His first male child, Clement Lionel Egerton, who was born in Farley, Staffordshire in 1880, would later enlist with the 2nd Light Horse Regiment of the First Australian Imperial Force and die from wounds at Gallipoli on 16 May 1915.