As composed by BluePyramid.org, whoever they are. Found via Mental Floss which lists several such lists. So naturally the first thing I did was search them all for Shakespeare, who appears on only this one. It's so hard to measure because you have to ask what "book" means. Is Hamlet a book? Or only a certain version? Are we talking about best loved, most read, most purchased?
Anyway, the BluePyramid list is my new best friend because it includes Hamlet(#2), Macbeth(#42), King Lear (#49), Romeo and Juliet (#62), Henry V(#199), The Winter's Tale (#304), The Tempest (#496), Othello (#530) and A Midsummer Night's Dream (#581).
Wait....Winter's Tale? That's ... different.
Anyway, their list is apparently dynamically compiled based on people entering their own personal top 25 and then scoring accordingly, 1 point for position 25, 25 points for position 1. So if you want to get Shakespeare an even better showing, go add your tuppence.