He was educated Rugby before matriculating to Oxford University in 1901.
He also played first-class cricket for Nottinghamshire. After leaving university he became a solicitor in Nottingham, and later a Clerk to Nottingham City Magistrates. Cartwright served in the British Armed Forces during the First World War, joing the Royal Marines.
He was made a Temporary Second Lieutenant in 1914, then Temporary Captain, before reaching the rank of Temporary Major in 1917.
Serving on the Western Front, Cartwright was highly decorated, twice mentioned in dispatches, a Defence Science Organisation and Croix de guerre. Cartwright first came to note as a rugby player while at Rugby, representing the school team
On entering Oxford he was selected as a freshman to join the University rugby team He played in four successive Varsity Matches from 1901–1904, all at forward, collecting his sporting "Blues".
While still a university student, Cartwright was selected for the England national team during the 1903 Home Nations Championship.
A miserable defeat on a boggy Saint Helen"s ground against Wales. Despite the loss, Cartwright was reselected for the remaining two games of the tournament. Both loses. He continued his international career throughout his time at Oxford, with two caps in the 1904 Home Nations Championship and all three of the 1905 Championship.
After leaving Oxford in the later half of 1905 he joined Nottingham, becoming the first player to be capped for England directly from the club
His first international cap while a Nottingham player saw him given the captaincy of the England team, in the 1905 encounter with New Zealand. This was followed by Cartwright"s last international, leading England against the same touring South Africans.
The game ended in a 3-3 draw. After retiring he became a referee and was President of the Rugby Football Union in 1928 and 1929.
Cartwright played his seven first-class cricket matches with Nottinghamshire between 1901 and 1904 as a right-handed batsman but could only manage 60 runs.