They were made by one of the Kakiemon potteries, which created the first enamelled porcelain in Japan,[1] and exported by the early Dutch East India Company.
The artists who made these figures had never seen a real elephant and had to work from drawings and sketches; possibly from Buddhist sources.
[1] Kakiemon ware was an important type of Japanese export porcelain, shipped to Europe by the Dutch East India Company between the ports of Imari and Amsterdam.
England had tried to establish a 'factory' (that is, a trading post) in Japan in 1613 under an agreement between King James I and the shōgun Tokugawa Hidetada but the initiative was abandoned in 1623.
In this brief period Chinese export porcelain largely dried up, and Japanese potters stepped in to fill the gap, including Kakiemon's new technique and style.
[3] This sculpture was featured in A History of the World in 100 Objects, a series of radio programmes that started in 2010 as a collaboration between the BBC and the British Museum.