In the 1930s in British newspapers, particularly '
The Times' and '
The Observer'. For a brief history of the earlier 'invention'/development of crosswords in general, click
http://members.tripod.com/holy_98/puzzlex.htm
On that web-page, you will see two key names - A F Ritchie and D S Macnutt - largely responsible between them for the creation of the various 'rules' that apply to cryptic crosswords...thus, in a sense, the inventors of the format. Do a Google search on these men for further information.