Bedknobs and Broomsticks was one of my favourite Disney movies as a child, but somehow I never got around to reading the books it was based on (two books, here combined in a single volume) until now. 
 The books are, of course, very different. The movie is set during WWII, with the children being sent into the countryside to avoid the London Blitz, and are housed with Miss Price, which I think makes for a stronger setting than merely having her be a neighbour of their great aunt, as she is in the books. 
 The character of Emilius Jones (or Brown, in the movie) is substantially different, being a resident of 17th century London in the books, whom the children meet on one of their adventures on the magical bed. He is not quite as much of a charlatan and con man as he is in the movie, though he is a professional necromancer who doesn't really believe in magic. 
 All of the children's adventures, and Miss Price's attitude towards magic are very different in the books than in the movie. In some ways I am glad they were changed. The adventure on the "cannibal" island, complete with stereotypical natives, is uncomfortable reading for a modern reader, and was best left out. 
 Intrasubstantiary Locomotion (Substitutiary Locomotion in the movie) plays a much smaller but still key role in the climax of the story, but no one ever turns into a rabbit. Miss Price and Carey are, over all, the strongest characters in the story. The books have a different but still bittersweet ending. 
 Very enjoyable and charming.