NOTE: This is the story behind the movie. If you haven't seen the movie, beware spoilers.
The King's Speech: How One Man Saved the British Monarchy
Mark Logue, David Conradi
This is a good, readable, not-very-deep book. Its strength is that it has a vast wealth of material to draw on; Mark Logue is Lionel Logue's grandson, and he managed to assemble a kind of family archive consisting of Lionel's diaries, letters, commonplace books, notes, keepsakes, photographs, and so forth. David Conradi, the co-author, is a reporter, and that's about how The King's Speech reads: as a well-written long newspaper story. It's not ground-breaking, but I liked it.
Now, the spoilers: the movie sexed up the plot a great deal. For excellent dramatic reasons, let me add--the truth doesn't usually make a good story (cf. The Imitation Game, a movie I very much enjoyed in spite of having previously read the book it was "based on"). A film made strictly from the book would run something like: prince meets speech therapist, prince improves very quickly, prince and speech therapist become amiable if not intimate (no "Bertie," you may be sure), prince becomes king, king gives many speeches without incident, partnership continues on same basis for many years, the end. No arguments, no controversy, and no dramatic leadup to THE speech.
The one place I will fault the movie a bit is that it actually lies about one thing. Lionel Logue was notable because he insisted that the causes of stammering were not psychological but physical--exactly the reverse of the film. I understand why they did it; movies about people and relationships are more interesting than movies about abdominal muscles. But it misrepresents Logue's achievement, all the same.