Posting again as I need to know more and was a little vague before.

Have just learnt I'll need a Teachers Permit to legaly teach in Thailand.

So how do I apply?

I have a degree in Physics and a 40 hour on line TEFL course certificate from a school based in the U.K.

I also have 10 months experience of teaching in a certain country which may be not too far from here and which I won't be able to mention or I'll be in trouble.

Will my degree and budget TEFL be sufficient to get?

Thanks.

Get a job in a school first and they should help you with the process.  Make sure they're legit otherwise there's nothing they can do.   This is the normal process rather than you getting a license first.