Question What is ONE book recommended for teachers doing their DELTA module 1 test?
This is a trick question. There is no ONE book recommended for the DELTA, unless you mean which is one book among many that you would recommend.
Module 1 of the DELTA aims to develop understanding of language, language teaching methodology and approaches to learning. Therefore I could recommend any number of books on these areas.
A good grammar and an ELT methodology book would do. Books like An A-Z of ELT
by Scott Thornbury, Grammar for English Language Teachers
by Martin Parrot, and of course the same book that's often used for the CELTA, Jeremy Harmer's The Practice of English Language Teaching with DVD (4th Edition) (Longman Handbooks for Language Teachers)
Other useful books could include: 'Techniques and Principles in Language Teaching' by Larsen Freeman or How Languages are Learned 4th edition (Oxford Handbooks for Language Teachers)
by Lightbown and Spada.
Cambridge don't recommend any specific texts. I suggest that you look at the EFL books recommended by the particular centre at which you wish to study. Most training centres recommend their own books. It's probably a good idea to look at these.
Considering the considerable cost of taking a TEFL diploma, it might be worth thinking about more than one book. The extra money, compared to the cost of the course, is small.
I've written more about TEFL diplomas
in general here.
Good luck with your TEFL diploma.