In August 1858, Britain and the United States of America were united by a submarine telegraph cable that spanned the Atlantic. The news of this great achievement was met in the cities of America with parades, fireworks and parties. New York was the centre of the festivities and saw military and civic processions, including a torchlight parade by the Firemen, a spectacle so brilliant it was depicted in this engraving created to celebrate the new cable uniting the Old and New Worlds.

PAG8264 Cable celebration

This image depicts a very American affair, not just because the American firemen are centre stage, but also because it depicts several American men as pillars of the achievement. You can see Benjamin Franklin, pioneer of the use of electricity; Samuel Morse, whose Morse Code was used to communicate on the telegraph line; Cyrus Field, founder of the New York, Newfoundland and London Electric Telegraph Company and Captain Hudson of the US warship Niagara, one of the steamships used to lay the cable. It's clear that these men did all have a role to play leading up to and during the 1858 laying, but the cable itself was predominately funded by Liverpool merchants and went through Ireland and Canada, strongholds of the British Empire. Consequently this image may not portray an accurate image of the relationship between America and Britain in laying the cable, but it does show who celebrated it the most and the ideals they associated with it.
This is just an example of the types of objects created to commemorate this great achievement of scientific and engineering ingenuity, and within the National Maritime Museum's collection there are many other clues as to how people celebrated and commemorated the laying of the submarine telegraph cables.
The Museum has many sections of submarine cable from a variety of telegraph lines, including some apparently from the 1858 Atlantic laying. It is not clear, however, whether any of these were sold as souvenirs - rather, they appear to have come from personal collections of people directly related to the cable industry. But from contemporary sources we do know that sections of cable were set in gold and sold as 'charms' in England, advertised in newspapers like the Illustrated London News and The Times. Furthermore, in America the company, Tiffany, spotted an opportunity and bought the surplus cable from the laying company, cutting it into small sections and mounting it with brass ferules. These were engraved with the Tiffany name and sold for fifty cents each.

MEC2282 cable medal 1858

As well as sections of cable, Tiffany also made commemorative medals like this one, although these don't appear to have been on general sale, but were commissioned by the Chamber of Commerce of New York to give to individuals who had had a role in the laying of the cable. It's a good reminder of the central role of business and trade in this venture.
Unfortunately the 1858 Atlantic cable's success was short-lived, and by mid-September it had stopped working completely, leaving many of these souvenirs redundant and rumours that the Atlantic cable had all been part of an elaborate hoax. The failure of the cable resulted in lost fortunes and a government enquiry that meant the next attempt at laying a submarine telegraph across the Atlantic wasn't made until nearly a decade later. But with the added glamour of the largest steamship in the world, the Great Eastern as the cable-laying ship, souvenirs for the 1866 Atlantic cable exploded onto the market, including a few that remembered the 1858 cable. One jug, for example, shows both the HMS Agamemnon, one of the ships involved in the 1858 cable-laying, along with the Great Eastern, the much celebrated vessel that helped make the 1866 laying a success.

ZBA4385 Great Eastern jug

Despite the 1858 failure, the feat of laying a cable across such a vast body of water was successful in capturing the public imagination, resulting in many souvenirs, books and artworks of the 1866 Atlantic cable. Some other examples can be seen in this NMM Library blog.