The stump, originally from Richmond Park, was moved to Kensington Gardens in 1928 and was declared a Grade-II listed structure in 1997. It was only after it was relocated that the illustrator Ivor Innes carved the figures into it.
Figures include Wookey the witch, Huckleberry the gnome, and Grumples and Groodles the Elves being awakened by Brownie, Dinkie, Rumplelocks and Hereandthere.
Pink Floyd's 1969 album Ummagumma features a picture of David Gilmour in front of the Elfin Oak and the comedian Spike Milligan was a lifelong fan, leading a successful campaign in 1996 to have it restored.
All the above information is lifted almost verbatim from http://en.wikipedia.org/wiki/Elfin_Oak but it is a Saturday so please forgive your author.