You have no entitlement here at all, regardless of the length of your service. The right to ask to work PT or to negotiate hours stems from legislation covering parents or adopters/carers of children.
�My employer has now said that they cannot cut my hours because it is not in the companies contract� doesn�t make sense to me. I suspect what you mean is they�ve said you�re contracted to 20 hours, so that�s what they would like you to do.
Your studies are the most important thing here. Redoing part or all of them is tedious and costly, so that has to be your priority.
Explain to them that you�d like to stay with them, but if they can�t be flexible you�ll have to find work elsewhere. If they value you they�ll bend. If they don�t, they won�t.
People leave jobs because they don�t suit each other all the time. Start looking for something else that allows you to get your degree.
Good luck.