Borrowing a book does not just have to happen in the library. In upper key stage 2 the children are encouraged to be involved in the Pass the book initiative. An unfamiliar book, little used in the library, is placed in a plastic wallet along with a small note book. A child then reads the book, writes a short comment and passes the book onto another person in the class; year 5 went through 4 books last year, you just have to keep a check on who has the book and remind them to keep it moving.
Similarly the infant classes have a Travelling book which goes home in a bag I made especially for the travelling books. Along with a quality text a small notebook and a simple game, based on the book, is placed in the bag. The children then take it home to share with their family and return it, passing it on to another child in the infants. I have made 5 of these travelling bags now and change the contents frequently.