What business or finance masters can I do with a third class honours BSc. degree in Physics?

You can do any of them provided you get a place. However it may be a bit difficult if you have a 3rd class degree as most masters require a 2nd class degree (2:1 in some cases especially for more popular ones.) But you never know if you can convince them that you are serious and committed you may get a place.

some courses will take students on as a Diploma (same as Masters but without the thesis at the end). If you reach a certain level during the course they will allow you to upgrade to a Masters by doing the thesis

well the worst thing you can do is not apply!! i was in the same boat as you and thought that i would never get in to a uni but a few rejections lateri got a place on a masters! so give it a shot.