Nothing Is Unbelievable Anymore.
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No best answer has yet been selected by lucemma4. Once a best answer has been selected, it will be shown here.
For more on marking an answer as the "Best Answer", please visit our FAQ.If there is nothing in your contract, and as this is a temporary position, you could effectively just leave without notice. However, if you are relying on them for a reference, I would give a minimum of one week notice up to as much as you can, although this is still no guarantee that they will give you a reference.
If you don't need a reference from them, I would just walk out when you are ready. As you said, they are a ruthless company so would probably do the same to you if they wanted to get rid of you.