Blagden, born in Wotton under Edge, studied medicine at Edinburgh, where one of his professors was Joseph Black, and graduated in 1768. He became a medical officer in the British army in the same year and theoretically remained in that post until 1814. From 1782 to 1789 Blagden was assistant to Henry Cavendish, a post that involved him in the so-called ‘water controversy’, a dispute between James Watt, Cavendish, and Antoine Lavoisier concerning the priority of the discovery of the synthesis of water from its elements. Blagden was friendly with the great French scientists of the day, especially Claude Berthollet, and on a visit to Paris in 1783 he told Lavoisier of Cavendish's synthesis, an experiment that Lavoisier repeated in Blagden's presence. Blagden became secretary of the Royal Society soon afterward, in which capacity he published Watt's papers on the same subject. The dispute was largely artificial because the three men drew different conclusions from their work.

Blagden's own scientific work was concerned with the freezing of mercury, the supercooling of water, and the freezing of salt solutions. He discovered, in 1788, that the lowering of the freezing point of a solution is proportional to the concentration of the solute present. This became known as Blagden's law. Blagden was knighted in 1792.