Are PhD students considered employees under employment rights law. I would like to know what legal avenues (and any other avenues) are available for a PhD student who is bullied by their supervisor.
I would also welcome any response from any PhD students who are and have been bullied by their supervisor for advice on how to deal with such a situation that occurs in the absence of witnesses.

Sorry to hear that you are having problems. Bullying does unfortunately occur in academia, as anywhere e.g. http://www.bullyonline.org/cases/case15.htm

You do have rights and certainly shouldn't accept bullying behaviour, for your sake and that of future staff/students.

Some advice here about workplace bullying: http://www.bullyonline.org/workbully/index.htm

You find it worth checking out your student handbook for information about grievance procedures.

Hope you can sort this, take care.

Unfortunately I have felt bullied by my supervior. I didn't even realise until I told another phd student about some of the incidents and she was able to see the situation from an outsiders perspective.
I think that when you start a phd you don't know what to expect and so when your sup goes too far, you don't know whether that is the norm for other students or not. I would suggest talking confidentialy to someone else. An outsiders perspective is priceless. As far as incidents with no witnesses go, this is a huge issue for me. My 1st sup has been very personal with me but when my second supervisor is there she's not as hostile. I suggest keeping a note of all these situations in as much detail as possible. You can take this to your head of dept or whoever is the most appropriate person who can change your supervisor (if that is what you want).