The Uncommon Reader by Alan Bennett, from LT/Good Reads category
Her Majesty the Queen is at home one day when the dogs decide to explore a bit and find the Mobile Library parked outside the palace kitchen. She investigates and feels that since she is there, the least she can do is borrow a book. She takes a book by an author she remembers meeting and feels obliged to read it.
This little act sets up a chain reaction that has quite the consequences. The Royal household is rather shaken to find Her Majesty reading when she ought to be doing Something Worthwhile.
There really isn't much more to this book than what I just said, but it's a short little book and rather amusing.