LKQCP LM Ireland 1868; MRCS Eng 1867; MRCPI 1903.
Greenhalgh was educated at Royal Manchester School of Medicine and was apothecary to the Honorable East India Companies and HM Indian Service before settling in general practice in Heaton-Norris, Manchester. Greenhalgh later moved to Buxton and was consultant surgeon to Manchester Warehousemen and Clerks' Orphan Schools and honorary (later consultant) surgeon at Stockport Infirmary.