BSc Manch 1917, DPH 1923, MB ChB 1929; MRCS LRCP 1919, MRCP 1930; DPM Camb 1921.
Kelly studied medicine at the University of Manchester where he was demonstrator of physiology. After qualifying, Kelly was house surgeon at Preston Royal Infirmary and at Ancoats Hospital Manchester before being appointed senior medical officer to the Special War Hospital, Tooting, in 1920. In 1921 Kelly was appointed medical superintendent at Brinnington Neurological Hospital and the following year was senior medical officer to Grangethorpe Hospital Manchester. From 1924 until 1930 Kelly was in general practice in Rusholme, Manchester. In 1928 Kelly returned to hospital practice being appointed honorary assistant physician to Manchester Victoria Memorial Jewish Hospital. Kelly was later honorary physician at the Jewish Hospital and at Manchester Hospital for Consumption. Kelly was a member of the British Psychology Society and of MMS.