Founded by William Shipley as the "Society of Arts" in Rawthmell's Coffee House. They carried on meeting in coffee houses and taverns but as the society grew they needed more space. Shipley rented a house in Craig's Court, SW1 and In February 1755 he rented out two rooms to the society. June 1756 the society moved to a house in Castle Court, Strand. In 1759 they purchased the lease of a warehouse in Denmark Court, north of the Strand and Sir William Chambers altered it to meet their needs.
In 1908 the society was granted permission to add "Royal" to the name.