Wright studied medicine at Oxford University and Guy's Hospital, London. In 1880 he was appointed resident surgical officer at MRI and promoted to honorary assistant physician in 1882. He remained on the MRI staff until 1911. Wright also worked at Royal Manchester Children's Hospital and became well-known for his paediatric work. He published Hip disease in childhood (1887) and with Henry Ashby,Textbook of diseases of children (1889), which was the standard work on the subject. In 1900 he was made professor of systematic surgery at Owens College Manchester and a full surgeon at MRI. He was much involved in the planning of the new MRI on Oxford Road. Wright was a successful teacher, and classes well-attended.