Whilst I agree with Systematic that a General English textbook is better than an exam text at this level, KET is a bit higher than false beginner. For example, OUP claims that students finishing Headway Elementary would be ready to take KET, presumably meaning that students finishing Headway Beginner (or the old Headstart) would not. Any other Elementary text would be okay, although ones published by British publishers such as Headway do seem to have sneakily had content connected to the exam such as street signs and some workbook exercise types put into them.
Apart from that, just get the students to buy a book of practice tests and emphasize the parts of the textbook that most tie in with the exam.
Here's a list I came across by Googling Cambridge KET textbookhttp://www.cambridgeesol.org.vn/?m=cambridge&catid=27