The first underwater electrical lines were put into place shortly after the invention of the working telegraph in 1839. In 1842, Samuel Morse submerged a wire (insulated with hemp and India rubber) in the water of the New York Harbor. The wire was able to able to successfully carry a telegraph signal. Shortly after, another insulating gum, Gutta-Percha, started to make its appearance.
In August 1850, the Anglo-French Telegraph Company laid the first line across the English Channel. This was also the first commercial underwater cable. It was simply a copper wire coated with Gutta-Percha.
By the 19th century, several submarine cables had already been constructed (see picture below). At this point, the outer layer of the cables was either iron or steel wire, which surrounded India Rubber and Gutta-Percha, which surrounded the core of multi-stranded copper.
Early cables like these had some severe electrical problems, however. The combined inductance and capacitance of such a long wire surrounded by water (or earth) was greatly retarding the electrical signal. Michael Faraday showed the relationship between the capacitance (of the wire and water/earth) and this retardation. At this point, cable designs failed to correct for these effects. A series of inventions and mathematical discoveries (many of which William Thompson was involved with) were able to mitigate the problems somewhat.