Turner was born in Jamaica but came to Edinburgh as a child. He received his MD from the University of Edinburgh in 1819 and also received his licence and fellowship from the Royal College of Physicians of Edinburgh in this year. Following this he left to study at Gottingen for two years and had a particular interest in chemistry and mineralogy. Upon his return to Edinburgh Turner instituted a course of lectures on chemistry. In 1828 when University College London opened he was appointed to the new Chair of Chemistry, a position which he held until his death. Turner felt that chemistry was too heavily based on hypothesis and that more concrete facts needed to be established, therefore he concerned himself with creating analytical methods through which the atomic weights of the elements could be determined.