Wrigley was educated at the University of Manchester and qualified in 1909. He decided to specialise in ENT work and was appointed to the honorary staff of Manchester Ear Hospital in 1913. In 1914 he was made aural surgeon to the Royal Schools for the Deaf, Manchester. He was elected to the honorary staff of MRI in 1927 and held this post until retirement in 1950. He published Observations on the Tonsil and Adenoid Problem and Foreign Bodies in the Air and Food Passages. He was the brother of Philip Wrigley.