Is there a way to see all the books a child has read?

Yes, if you click on the child's name on the Pupil Reading page you can see lots of information about a specific child. 

If you click on the bookshelf tab you can see all of the books added to a child's bookshelf. To see more information about each book click on the arrow and the information hidden will expand. 

There's a green load more button, which will let you go back over time. The most recent books will show at the top of the page.