Watson, the son of a London tradesman, was apprenticed to an apothecary from 1731 to 1738. After working for many years at that trade, Watson was made a licentiate of the Royal College of Physicians. This was later followed in 1762 with an appointment as physician to the Foundling Hospital.

Watson had a great interest in natural history and was instrumental in introducing the Linnaean system of botanical classification into Britain. He is, however, mainly remembered for his account of the nature of electricity. This was based on a series of experiments with the Leyden jar, discovered by Pieter van Musschenbroek in 1746. Watson not only improved the device by coating the inside of it with metal foil but also realized that the pattern of discharge of the jar suggested that electricity was simply a single fluid or, as he termed it, an ‘electrical ether’. Normally bodies have an equal density of this fluid so that when two such bodies meet there will be no electrical activity. If, however, their densities are unequal the fluid will flow and there will be an electric discharge. That is, electricity can only be transferred from one body to another; it cannot be created or destroyed. Such a theory was also developed with greater depth at about the same time by Benjamin Franklin and was to emerge as the orthodox position by the end of the century.

Watson also made an early and unsuccessful attempt in 1747 to measure the velocity of electricity over a four-mile (6.4-km) circuit. Although it appeared to complete its journey in no time at all Watson sensibly concluded that it probably traveled too fast to be measured.