The best book about the history of English language teaching is by A.P.R Howatt, 

A History of English Language Teaching

In it he details everything you could ever wish to know about the direct method! 

In summary;

1. Before professional language teaching, most European languages were learnt in a "direct" way, although it was not called that. Instead people talked about "picking up" a language. 
2. This was in contrast to Latin and Greek, which were learnt from books and in large classes with teachers.
3. Many "methods" were introduced for learning European languages, and language learning became more popular throughout the 19th century, as travel became more common and affordable.
4. Maximillian Berlitz did not invent the direct method, but he did popularise it throughout the world. Sadly, the Berlitz organisation subsequently gave up using direct methods in many of its schools.
5. Robin Callan invented the Callan Method after teaching in a Berlitz school in Italy. He significantly improved the layout of the method and introduced many innovations, meaning that the Callan Method is also an audio-lingual method, not just a direct method. He also extended the methodology beyond the beginning stages and created a syllabus all the way to the First Certificate.
6. You can read an anonymous version of Mr Callan's life work here. (Its not been edited very well, sorry!). This story is just speculation, we don't know if it's true.
7. The Avalon school in London created a version of the Callan method, but their innovation was to let students freely answer the questions. This is quite different to the Callan method where all answers are tightly scripted. Mr Callan claims that the Avalon method is a copy of the Callan method and that the director of the Avalon school had the idea to copy the method after doing building work for the Callan School! 
8. A Polish company called "Direct English Publishers" are currently involved in a legal dispute with the Callan Method organisation. . The Callan Method organisation claim that Direct English Publishers have plagiarised the Callan Method. You can read more about this here; http://www.callan.co.uk/en/news/