Peter Llewelyn Davies was the middle of five sons of Arthur and Sylvia Llewelyn Davies, one of the Llewelyn Davies boys befriended and later informally adopted by J. M. Barrie. Barrie publicly identified him as the source of the name for the title character in his 1904 play Peter Pan, or The Boy Who Wouldn't Grow Up.

The Davies boys were the inspiration for the stories of Peter Pan by J. M. Barrie, in which several of the characters were named after them. They were the sons of Sylvia (1866–1910) and Arthur Llewelyn Davies (1863–1907). Their mother was a daughter of French-born cartoonist and writer George du Maurier and sister of actor Gerald du Maurier, whose daughter was author Daphne du Maurier. Their father was a son of preacher John Llewelyn Davies, and brother of suffragist Margaret Llewelyn Davies.