Which academy was founded in London in 1660 to promote and encourage the works and ideas of scientists?

The Royal Society. The full name of the group when it originated was "The President, Council and Fellows of the Royal Society of London for Improving Natural Knowledge." The group of science-minded men began their organization in 1660 and sought and received a charter of incorporation from King Charles II in 1662. Some of the key people in getting the group started were Christopher Wren and Robert Boyle. While the Royal Society had official endorsement from the king and to this day continues to have the blessing of the British government, it was and is an voluntary organization, not a government agency. During the Scientific Revolution, the Royal Society served as a clearinghouse of knowledge and a network to connect those pursuing scientific discovery. A great book that shows the role the Royal Society played in the Scientific Revolution is: Ingenious Pursuits: Building the Scientific Revolution, by Lisa Jardine (1999).