William Coulson (1802 – 1877) was an English surgeon.
The younger son of Thomas Coulson, master painter in Devonport dockyard, he was born at Penzance; Walter Coulson was an elder brother. His father was a close friend of Sir Humphry Davy; his mother was Catherine Borlase. After receiving some classical education at the local grammar school, Coulson spent two years in Brittany (1816–18), studying the French language and literature. Having first been apprenticed to a Penzance surgeon, he entered Edward Grainger's School of Anatomy in the Borough, and attended St. Thomas's Hospital, where he became dresser to Frederick Tyrrell. He then studied in Berlin, where he knew the poet Thomas Campbell, and spent some months in Paris.
Coulson returned to London, and became a member of the Royal College of Surgeons on 26 September 1826. He helped found the Aldersgate Street School of Medicine with Tyrrell, Sir William Lawrence, and others, and acted for three years as demonstrator of anatomy. In 1828 he was elected surgeon to the Aldersgate Street Dispensary, and in 1830 consulting surgeon to the City of London Lying-in Hospital. In 1832 he, with his colleagues, resigned his connection with the Aldersgate Dispensary in a quarrel with the committee. In the same year he joined the medical board of the Royal Sea-bathing Infirmary at Margate.
In 1833 Coulson failed to secure election to an assistant-surgeoncy at the London Hospital, being beaten by Thomas Blizard Curling. His practice increased with his publications, He moved from his early residence in Charterhouse Square to a house in Frederick's Place, Old Jewry, where he had for many years perhaps the largest city practice.