Sometimes you open a book and are surprised that you haven't read it before. I would go further with John Kenrick's Musical Theatre: A History and admit to bafflement as to why I have not been recommending it to my students since it was first published in 2008. This second edition has been completely updated, with additional material covering 2010 to the present and should probably be on any self-respecting drama department's shelf. Although the book is water-tight in terms of its academic credentials – Kenrick is a Professor at New York University's Steinhardt School – the prose is narrative and light. Even the most reluctant A Level or IB student would find it easy to follow.
Kenrick begins his history in Ancient Greece and the first chapter, which covers Aristophanes to The Beggars Opera, is as good a general introduction to European Theatre for 16-18 year olds as I have read. It would be a fantastic starting point for an IB candidate wanting to focus on Musical Theatre, though I will use it to help those candidates who love their Musicals but struggle to shape that love into a more serious look at the mechanics of the art form. It is accessible, clear and detailed. There is an enticing and concisely-annotated suggested further reading section, as well as Kenrick's Musicals101.com website, which is a significant resource in its own right. Kenrick makes the history of the societies that shaped Musical Theatre compelling.