The character was in the initial version of the Sword in the Stone. The Once and Future King has a revised version without Madam Mim along with other modifications. The Once and Future King is not a novel but a collection of four previously published works. It is also missing the beautiful finale: The Book of Merlyn.
You can still buy the Sword in the Stone as a standalone novel, which will be the original version and includes the character. I bought an illustrated copy for my son.