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. On the right hand side of the book tile there's an expandable arrow, where you can find out more details about a child's reading.