Wow! What an exciting opportunity - but one fraught with peril! You're in the thick of it now, and won't have much time for theorizing.
I'd get a nice, basic, very clear and somewhat repetitive textbook - even if you end up not using it that much, it should give you some idea of how grammar can be sequenced and practiced. Something like the third edition of
Side By Side is kind of what I am thinking of here (but be aware that you would need to work through the FOUR volumes to get to a higher intermediate level, and that it may contain a few too many Americanisms for your tastes and purposes). I used it with small classes that often ended up as 1-2-1 (when students couldn't come), and it seemed to do the trick.
http://www.eltnews.com/features/intervi ... sky1.shtml
Alternatively, you might want to get a more "glossy" textbook with audiotapes etc (
Side By Side can end up seeming a little divorced from the real, complex real-life world). Perhaps the
New Cambridge English Course would be a good choice (because it presents typically "British" situations, accents etc)? I prefer its layout (one page per lesson, eminently achievable) to more recent, flashier contenders, and I think you can trust Michael Swan when it comes to grammar (the vocabulary to be reviewed is also highlighted). Are you going to attempt to forge links with the other school subjects/teachers, by the way (including English Language, and English Literature)?
Talking of Swan, he was one of the authors of
Learner English (now in a second edition). I am sure it has a chapter on Thai learners and what difficulties one might predict they will have in learning English (such as pronunciation/making the sounds, grammar/syntax, script/writing systems etc).
For vocabulary, something like CUP's
Essential Vocabulary in Use would be useful, at least for review/homework - as would, for grammar, Murphy's
Essential Grammar in Use). A nice picture dictionary would be nice, too (Oxford publish several in English/Thai editions).
Regarding pronunciation, don't work at it too hard unless and until it seems necessary (or, if you want to "review" the sounds of English before beginning a textbook, perhaps to e.g. teach the IPA for the more difficult sounds, at least do it snappily!). Cambridge's
English Pronunciation in Use looked good, but it may be a little too difficult for beginners and would thus require some adaptation (also just found this when searching for the previous title:)
http://international.ouc.bc.ca/pronunciation/
I know that is a lot of books, and you are more asking for ideas for approaches/lessons for 1-2-1 (besides which, your school may not have any money budgeted for this specific need), but I just got a little worried when you said, "I'm sure I can show her magazines and pictures and teach her nouns like that, and do the time and numbers fairly easily, but something more interesting would be nice!". I think there's gotta be a lot more structure and aims in this girl's learning for her to make consistent, assured progress is all.
Actually, to be honest, I can't really recommend any 1-2-1 methodology books to you; none of the ones presently available really address your specific situation (LTP's concerns more Business English, and Longman's, whilst also interesting, is more for independent expat teachers), time is short as I've said, and to realize wonderful things given this opportunity I guess you've ultimately gotta put the books away and listen to your heart, and this girl! I personally prefer reading books on vocabulary research and acquisition, and leaving the exact pedagogy more "up in the air", at least until key language has been identified, and materials/lessons developed on that basis (there is a natural methodology
within the language itself, that is, the contexts in which the language was and is used can and perhaps should be recreated - as far as possible - in "classroom" interaction).
So, I would have or buy something like the above stuff as a minimum, to show committment, help set goals etc, but be ready to set it all aside if the girl seems bright and able to pick up and retain things during more informal encounters. Lastly, even though she is in the UK and there is a lot she HAS TO learn, don't forget where she's from or the power of memory and the imagination.
Thanks for the reply - that was very comprehensive and useful! I put in a request today for the New Cambridge level one books, but I don't hold out much hope of them being purchased for just one student, UK school budgets being what they are (i.e. completely inflexible, with most of the money ring fenced for useless expensive stuff like a plasma screen in the entrance hall, and the head telling me there's no money to by chairs to replace the broken ones in my classroom 
- oops sorry 
rant over). 
). 
That being said, I do like the thought of "letting rip" with dramatic histrionics in classes (not sure if all my future students will, though...) 