I think it depends on whether you are receiving a financial gain, i.e. this is your business. If its a hobby then it is not required (I believe).
And it's not just a matter of getting a permit number, you would need a certificate of competence for the given type of livestock you are transporting, this means taking a course.
If in doubt ring your local animal health department / trading standards, and they will tell you all you need to know.